songyc/Logseq
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Logseq/Major Study/assets/3장_4가지_기본_부분공간_1785222523974_0.edn

1903 lines
106 KiB
Clojure
Executable File
Raw Blame History

{:highlights [{:id #uuid "6a685a78-846c-4c02-976a-445b78c8c392",
:page 2,
:position {:bounding {:x1 401.4135907627642,
:y1 80.0426025390625,
:x2 546.621537540108,
:y2 95.25711059570312,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 401.4135907627642,
:y1 80.0426025390625,
:x2 546.621537540108,
:y2 95.25711059570312,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "벡터공간 (vector space)'"},
:properties {:color "yellow"}}
{:id #uuid "6a685a7d-a9fc-46fd-aa0a-ddf6c8f3818f",
:page 2,
:position {:bounding {:x1 392.68901190534234,
:y1 248.67410278320312,
:x2 530.2173627354205,
:y2 263.8886413574219,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 392.68901190534234,
:y1 248.67410278320312,
:x2 530.2173627354205,
:y2 263.8886413574219,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "행렬공간(matrix space)"},
:properties {:color "yellow"}}
{:id #uuid "6a685a81-3e9f-4f22-8dcf-4ff3597a7ffa",
:page 2,
:position {:bounding {:x1 550.4920209385455,
:y1 248.67410278320312,
:x2 713.441850040108,
:y2 263.8886413574219,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 550.4920209385455,
:y1 248.67410278320312,
:x2 713.441850040108,
:y2 263.8886413574219,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "함수 공간(function space "},
:properties {:color "yellow"}}
{:id #uuid "6a685a91-40b4-4ff2-9376-66433c61d86e",
:page 2,
:position {:bounding {:x1 333.4474957920611,
:y1 282.5620422363281,
:x2 621.1751264072955,
:y2 297.0158386230469,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 333.4474957920611,
:y1 282.5620422363281,
:x2 621.1751264072955,
:y2 297.0158386230469,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "Ar= 0 을 만족하는 벡터들만 모아서 벡터 공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685a96-8151-425c-aff1-8f76ab7b3205",
:page 2,
:position {:bounding {:x1 185.55764899030328,
:y1 312.0758361816406,
:x2 368.27446112409234,
:y2 326.5296325683594,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 185.55764899030328,
:y1 312.0758361816406,
:x2 368.27446112409234,
:y2 326.5296325683594,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "행렬 A 의 영 공간 (null space)"},
:properties {:color "yellow"}}
{:id #uuid "6a685b10-625e-4ab7-a79f-76f40b0f0ba6",
:page 2,
:position {:bounding {:x1 173.50489935651422,
:y1 516.0454406738281,
:x2 240.30549750104547,
:y2 531.2599182128906,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 173.50489935651422,
:y1 516.0454406738281,
:x2 240.30549750104547,
:y2 531.2599182128906,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "기저(basis)"},
:properties {:color "yellow"}}
{:id #uuid "6a685b18-d976-44bd-b7b6-d36e4770223b",
:page 2,
:position {:bounding {:x1 405.7758649326861,
:y1 516.0454406738281,
:x2 627.7930463291705,
:y2 531.2599182128906,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 405.7758649326861,
:y1 516.0454406738281,
:x2 627.7930463291705,
:y2 531.2599182128906,
:width 793,
:height 1121.5281146896566}),
:page 2},
:content {:text "공간 을 완벽하게 설명하는 벡터 집합"},
:properties {:color "yellow"}}
{:id #uuid "6a685b7a-0ff6-487b-981b-a5c9c0b4f61c",
:page 3,
:position {:bounding {:x1 96.98064551129937,
:y1 393.0812530517578,
:x2 696.0156415440142,
:y2 437.0725860595703,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 526.1488202549517,
:y1 393.0812530517578,
:x2 696.0156415440142,
:y2 407.53504943847656,
:width 793,
:height 1121.5281146896566}
{:x1 96.98064551129937,
:y1 423.37953186035156,
:x2 257.0815289951861,
:y2 437.0725860595703,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "벡터공간 R\"에서 선형결합 cut dw를 만들 수 있다"},
:properties {:color "yellow"}}
{:id #uuid "6a685b91-372b-4f20-877a-8ba6ef77f1ca",
:page 3,
:position {:bounding {:x1 186.27082953229547,
:y1 493.4970245361328,
:x2 279.9757245518267,
:y2 508.71156311035156,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 186.27082953229547,
:y1 493.4970245361328,
:x2 279.9757245518267,
:y2 508.71156311035156,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "3.1 절 연습 문제"},
:properties {:color "yellow"}}
{:id #uuid "6a685b9e-e75d-4c95-804f-f5a1678ddea6",
:page 3,
:position {:bounding {:x1 238.5231793858111,
:y1 565.5282745361328,
:x2 559.529496524483,
:y2 581.5034942626953,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 238.5231793858111,
:y1 565.5282745361328,
:x2 559.529496524483,
:y2 581.5034942626953,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "모든 선형 결합 cu+dw 가 벡터 공간에 속해야 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a685bea-1fd1-4023-b61a-7fe416a1142e",
:page 3,
:position {:bounding {:x1 95.86332831159234,
:y1 859.3823699951172,
:x2 691.9038251377642,
:y2 903.9918060302734,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 580.5526288487017,
:y1 859.3823699951172,
:x2 691.9038251377642,
:y2 874.5968475341797,
:width 793,
:height 1121.5281146896566}
{:x1 95.86332831159234,
:y1 888.7772674560547,
:x2 361.8558515049517,
:y2 903.9918060302734,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "영 벡터 0= ( 0, 0 ,・, 0 )만 포함된 공간 2 도 부분공간이다 ."},
:properties {:color "yellow"}}
{:id #uuid "6a685bff-7504-4c04-b67a-18e58fa0f1ef",
:page 3,
:position {:bounding {:x1 245.1082166172564,
:y1 918.1722259521484,
:x2 435.91963324323297,
:y2 933.3867034912109,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 245.1082166172564,
:y1 918.1722259521484,
:x2 435.91963324323297,
:y2 933.3867034912109,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "Z 는 가장 작은 벡터공간이다 "},
:properties {:color "yellow"}}
{:id #uuid "6a685c11-eeec-447d-a392-e985bf0f02ee",
:page 3,
:position {:bounding {:x1 508.69966254010797,
:y1 918.1722259521484,
:x2 621.977494571358,
:y2 933.3867034912109,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 508.69966254010797,
:y1 918.1722259521484,
:x2 621.977494571358,
:y2 933.3867034912109,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "가역행렬의 영 공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685c2b-abee-4e34-9ae6-52cbbb35664a",
:page 3,
:position {:bounding {:x1 94.757897708565,
:y1 947.0084686279297,
:x2 684.593705508858,
:y2 992.4261322021484,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 128.5388806797564,
:y1 947.0084686279297,
:x2 684.593705508858,
:y2 965.2658538818359,
:width 793,
:height 1121.5281146896566}
{:x1 94.757897708565,
:y1 977.9723968505859,
:x2 193.91920599713922,
:y2 992.4261322021484,
:width 793,
:height 1121.5281146896566}),
:page 3},
:content {:text "Az =0 의 유일한 해 가 영 벡터 z= 0이라면, 행렬 A 의 열 들은 선형 독립이고 , 행렬 A 의영 공간은 Z 이다"},
:properties {:color "yellow"}}
{:id #uuid "6a685c56-722c-4f5e-9f80-694676540d08",
:page 4,
:position {:bounding {:x1 127.98022589460015,
:y1 81.05294799804688,
:x2 294.56144842877984,
:y2 96.2674560546875,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 127.98022589460015,
:y1 81.05294799804688,
:x2 294.56144842877984,
:y2 96.2674560546875,
:width 793,
:height 1121.5281146896566}),
:page 4},
:content {:text "행렬 로 이루어진 벡터공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685c58-34f6-446e-b8c2-6658ceb88834",
:page 4,
:position {:bounding {:x1 127.98022589460015,
:y1 280.31553649902344,
:x2 290.7435468174517,
:y2 294.7693328857422,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 127.98022589460015,
:y1 280.31553649902344,
:x2 290.7435468174517,
:y2 294.7693328857422,
:width 793,
:height 1121.5281146896566}),
:page 4},
:content {:text "함수 로 이루어진 벡터공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685c82-f0dc-4b07-b52a-50873b06fb37",
:page 4,
:position {:bounding {:x1 130.20295843854547,
:y1 556.1024017333984,
:x2 731.223832461983,
:y2 602.5066375732422,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 509.7785504795611,
:y1 556.1024017333984,
:x2 731.223832461983,
:y2 574.3597869873047,
:width 793,
:height 1121.5281146896566}
{:x1 130.20295843854547,
:y1 587.2921600341797,
:x2 522.0338300205767,
:y2 602.5066375732422,
:width 793,
:height 1121.5281146896566}),
:page 4},
:content {:text "공간' 이라는 단어 는 벡터 나 행렬 또는 함수의 모든 선형결합이 공간 안에서 닫혀있음 을 의미 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a685cbb-c5e0-4cbc-9217-fb9d6b9730cf",
:page 4,
:position {:bounding {:x1 130.20295843854547,
:y1 684.7958221435547,
:x2 727.456010196358,
:y2 762.6513519287109,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 130.20295843854547,
:y1 684.7958221435547,
:x2 727.450394961983,
:y2 700.0102996826172,
:width 793,
:height 1121.5281146896566}
{:x1 130.20295843854547,
:y1 715.3199310302734,
:x2 727.456010196358,
:y2 729.7737274169922,
:width 793,
:height 1121.5281146896566}
{:x1 130.20295843854547,
:y1 748.1975555419922,
:x2 542.271684024483,
:y2 762.6513519287109,
:width 793,
:height 1121.5281146896566}),
:page 4},
:content {:text "행렬 과 함수를 벡터 로 생각할 필요가 있다. 그러나 대부분 우리가 가정하는 벡터는 열벡터 이다.이들은 \" 개의 성분 을 가진 벡터이다(그러나 \"개의 성분 을 가진 모든 벡터가 아닐 수도 있다). R\" 의 내부에는 중요한 벡터 공간이 있고 , 이들은 R\" 의 부분공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685ce3-0cf7-4dcd-8c92-9cca6577bf83",
:page 4,
:position {:bounding {:x1 131.32028326764703,
:y1 853.8789978027344,
:x2 726.6595014072955,
:y2 904.1225280761719,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 472.1491864658892,
:y1 853.8789978027344,
:x2 726.6595014072955,
:y2 871.3757019042969,
:width 793,
:height 1121.5281146896566}
{:x1 131.32028326764703,
:y1 885.8651428222656,
:x2 321.6205914951861,
:y2 904.1225280761719,
:width 793,
:height 1121.5281146896566}),
:page 4},
:content {:text "3 차원 공간의 원점을 지나는 평면 은 R ' 처럼 보이 더라도 R' 과 다르다. "},
:properties {:color "yellow"}}
{:id #uuid "6a685d18-0e9e-402f-89ed-9eb0662e72e5",
:page 5,
:position {:bounding {:x1 100.22561774030328,
:y1 96.6478271484375,
:x2 238.55420050397515,
:y2 111.10162353515625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 100.22561774030328,
:y1 96.6478271484375,
:x2 238.55420050397515,
:y2 111.10162353515625,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "정의 부분공간 판정법"},
:properties {:color "yellow"}}
{:id #uuid "6a685d1b-f3e8-43f5-b6cd-0903f6630ec6",
:page 5,
:position {:bounding {:x1 132.90117010846734,
:y1 198.75146484375,
:x2 326.9575360752642,
:y2 217.0089111328125,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 132.90117010846734,
:y1 198.75146484375,
:x2 326.9575360752642,
:y2 217.0089111328125,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "o+w가 부분공간 안에 있다 ."},
:properties {:color "yellow"}}
{:id #uuid "6a685d1e-aaf7-4f8b-b0b3-080ef1880e6e",
:page 5,
:position {:bounding {:x1 132.90117010846734,
:y1 230.16705322265625,
:x2 299.5709393955767,
:y2 247.66375732421875,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 132.90117010846734,
:y1 230.16705322265625,
:x2 299.5709393955767,
:y2 247.66375732421875,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "cu가 부분 공간 안에 있다."},
:properties {:color "yellow"}}
{:id #uuid "6a685d5f-2eac-4706-b398-6effddda1d5f",
:page 5,
:position {:bounding {:x1 484.74870428815484,
:y1 450.7537536621094,
:x2 539.7522748447955,
:y2 465.2075500488281,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 484.74870428815484,
:y1 450.7537536621094,
:x2 539.7522748447955,
:y2 465.2075500488281,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "부분 집합"},
:properties {:color "yellow"}}
{:id #uuid "6a685d61-ef97-4afe-be47-b5dcfc5a4e8a",
:page 5,
:position {:bounding {:x1 560.9638837315142,
:y1 450.7537536621094,
:x2 616.5545819737017,
:y2 465.2075500488281,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 560.9638837315142,
:y1 450.7537536621094,
:x2 616.5545819737017,
:y2 465.2075500488281,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "부분공간"},
:properties {:color "yellow"}}
{:id #uuid "6a685f94-50c8-45aa-80bb-e3fbf70094ff",
:page 5,
:position {:bounding {:x1 263.59147772565484,
:y1 524.9126281738281,
:x2 487.3051618076861,
:y2 539.3664245605469,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 263.59147772565484,
:y1 524.9126281738281,
:x2 487.3051618076861,
:y2 539.3664245605469,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "모든 부분공간 이 영벡터를 포함 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a685fa3-8906-4e6d-aa25-e21a89cd56df",
:page 5,
:position {:bounding {:x1 90.39561590924859,
:y1 524.9126281738281,
:x2 691.6971600987017,
:y2 568.7613220214844,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 579.518510196358,
:y1 524.9126281738281,
:x2 691.6971600987017,
:y2 539.3664245605469,
:width 793,
:height 1121.5281146896566}
{:x1 90.39561590924859,
:y1 554.3075866699219,
:x2 420.46037421002984,
:y2 568.7613220214844,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "R의 평면이 부분공간이 되기 위해서는 원점 ( 0, 0, 0 )을 지나야 한다."},
:properties {:color "yellow"}}
{:id #uuid "6a685fbe-80ec-475f-a6f0-7c084844527d",
:page 5,
:position {:bounding {:x1 160.0971082188189,
:y1 683.9043273925781,
:x2 389.6579755283892,
:y2 698.3581237792969,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 160.0971082188189,
:y1 683.9043273925781,
:x2 389.6579755283892,
:y2 698.3581237792969,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "원점을 지나는 직선도 부분공간이다 "},
:properties {:color "yellow"}}
{:id #uuid "6a685fc9-dd2d-46fe-bedd-c9c2fbd6350d",
:page 5,
:position {:bounding {:x1 141.62573370710015,
:y1 759.0735168457031,
:x2 303.06599554792047,
:y2 773.5273132324219,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 141.62573370710015,
:y1 759.0735168457031,
:x2 303.06599554792047,
:y2 773.5273132324219,
:width 793,
:height 1121.5281146896566}),
:page 5},
:content {:text "부분공간은 전체 공간 R "},
:properties {:color "yellow"}}
{:id #uuid "6a686013-b0c5-4a4a-9af9-2e62a71aec55",
:page 6,
:position {:bounding {:x1 150.65934881940484,
:y1 523.236686706543,
:x2 705.817094180733,
:y2 541.4940719604492,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 150.65934881940484,
:y1 523.236686706543,
:x2 705.817094180733,
:y2 541.4940719604492,
:width 793,
:height 1121.5281146896566}),
:page 6},
:content {:text "벡터 U. w를 포함하는 부분공간은 반드시 모든 선형 결합 cut dw 를 포함해야 한다."},
:properties {:color "yellow"}}
{:id #uuid "6a686043-c0fb-47b0-b4be-71687288d476",
:page 6,
:position {:bounding {:x1 140.82934698835015,
:y1 897.7514495849609,
:x2 465.18379339948297,
:y2 915.2481536865234,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 140.82934698835015,
:y1 897.7514495849609,
:x2 465.18379339948297,
:y2 915.2481536865234,
:width 793,
:height 1121.5281146896566}),
:page 6},
:content {:text "항등 행렬 / 자체가 부분공간 이 될까 ? 물론 아니다 "},
:properties {:color "yellow"}}
{:id #uuid "6a68606d-599d-49cc-8d11-c9242f09c4c4",
:page 7,
:position {:bounding {:x1 93.96151861920953,
:y1 147.1409912109375,
:x2 694.7110761143267,
:y2 194.63885498046875,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 667.3823407627642,
:y1 147.1409912109375,
:x2 694.7110761143267,
:y2 164.6376953125,
:width 793,
:height 1121.5281146896566}
{:x1 93.96151861920953,
:y1 178.66357421875,
:x2 510.09614691510797,
:y2 194.63885498046875,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "A와의 곱으로 나타낼 수 있는 벡터 b 는 행렬 A의 ' 열공간'을 형성"},
:properties {:color "yellow"}}
{:id #uuid "6a68607f-254b-4136-989c-36476ffc0843",
:page 7,
:position {:bounding {:x1 94.99562964215875,
:y1 222.2032470703125,
:x2 304.76042303815484,
:y2 237.41778564453125,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 94.99562964215875,
:y1 222.2032470703125,
:x2 304.76042303815484,
:y2 237.41778564453125,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "Ar는 행렬 A의 열 들의 선형 결합"},
:properties {:color "yellow"}}
{:id #uuid "6a686094-5515-45fb-9c86-80a140690178",
:page 7,
:position {:bounding {:x1 93.96151861920953,
:y1 252.7154541015625,
:x2 691.2500775791705,
:y2 297.69342041015625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 605.1335614658892,
:y1 252.7154541015625,
:x2 691.2500775791705,
:y2 267.92999267578125,
:width 793,
:height 1121.5281146896566}
{:x1 93.96151861920953,
:y1 283.2396240234375,
:x2 519.9149335362017,
:y2 297.69342041015625,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "이 선형 결합은행렬 A의 열공간을 생성 한다. 이는 열 벡터로 구성된 벡터 공간이다"},
:properties {:color "yellow"}}
{:id #uuid "6a6860b8-2498-411e-a1d4-039ab1fd7035",
:page 7,
:position {:bounding {:x1 105.94294867292047,
:y1 370.6398620605469,
:x2 375.7552350498736,
:y2 385.0935974121094,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 105.94294867292047,
:y1 370.6398620605469,
:x2 375.7552350498736,
:y2 385.0935974121094,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "열공간 은 모든 열의 선형결합 으로 구성 된다"},
:properties {:color "yellow"}}
{:id #uuid "6a6860bb-f4e0-4c16-8617-210602bad98f",
:page 7,
:position {:bounding {:x1 507.9033063389361,
:y1 370.6398620605469,
:x2 643.8777020908892,
:y2 385.0935974121094,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 507.9033063389361,
:y1 370.6398620605469,
:x2 643.8777020908892,
:y2 385.0935974121094,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "가능한 모든 벡터 Az"},
:properties {:color "yellow"}}
{:id #uuid "6a6860c1-eeb6-4a60-83d5-6a48b9d272cb",
:page 7,
:position {:bounding {:x1 143.05209479108453,
:y1 401.2709045410156,
:x2 354.9720624424517,
:y2 415.7247009277344,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 143.05209479108453,
:y1 401.2709045410156,
:x2 354.9720624424517,
:y2 415.7247009277344,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "Ar 들이 열공간 C( A) 를 채운다."},
:properties {:color "yellow"}}
{:id #uuid "6a6860d3-efc3-4506-a1d2-ad1b12720150",
:page 7,
:position {:bounding {:x1 243.59864935651422,
:y1 573.7179260253906,
:x2 545.0276044346392,
:y2 616.9247741699219,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 243.59864935651422,
:y1 573.7179260253906,
:x2 545.0276044346392,
:y2 587.4109802246094,
:width 793,
:height 1121.5281146896566}
{:x1 244.6327527500689,
:y1 603.2317199707031,
:x2 543.9907392002642,
:y2 616.9247741699219,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "방정식 Az=b 의 해 가 존재할 필요충분조건은벡터 6 가 행렬 A의 열공간 안에 있는 것이다."},
:properties {:color "yellow"}}
{:id #uuid "6a6860eb-b4f8-478f-99f2-5be30d4bd98a",
:page 7,
:position {:bounding {:x1 94.99562964215875,
:y1 658.3249359130859,
:x2 690.2159589268267,
:y2 703.0413055419922,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 94.99562964215875,
:y1 658.3249359130859,
:x2 690.2159589268267,
:y2 673.5394134521484,
:width 793,
:height 1121.5281146896566}
{:x1 94.99562964215875,
:y1 687.8268280029297,
:x2 313.53569159284234,
:y2 703.0413055419922,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "벡터 6가 열공간 C (A ) 안에 있을 때, b 는 행렬 A의 열들의 선형 결합 이다 . 이때 선형 결합의계수는 방정식 Azr=b 의 해가 된다"},
:properties {:color "yellow"}}
{:id #uuid "6a686110-e6d3-4d7d-a15d-1781c70e4791",
:page 7,
:position {:bounding {:x1 93.96151861920953,
:y1 762.1045379638672,
:x2 691.423051211983,
:y2 837.4639739990234,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 174.76484808698297,
:y1 762.1045379638672,
:x2 689.6692059971392,
:y2 777.3190765380859,
:width 793,
:height 1121.5281146896566}
{:x1 93.96151861920953,
:y1 792.7356414794922,
:x2 691.423051211983,
:y2 807.9501800537109,
:width 793,
:height 1121.5281146896566}
{:x1 94.99562964215875,
:y1 822.2494354248047,
:x2 131.27273688092828,
:y2 837.4639739990234,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "행렬 A 의 열만 모으면 이는 부분공간을 형성 하지 않는다는 것이다. 가역 행렬은 부분공간을 형성하지 않는다. 특이행렬 도 부분공간 을 형성하지 않는다 . 모든 선형결합 을 포함 해야한다. "},
:properties {:color "yellow"}}
{:id #uuid "6a686148-a398-42de-8cf8-40c16d4fc2a1",
:page 7,
:position {:bounding {:x1 94.99562964215875,
:y1 922.1065521240234,
:x2 344.0450299717486,
:y2 939.6032562255859,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 94.99562964215875,
:y1 922.1065521240234,
:x2 344.0450299717486,
:y2 939.6032562255859,
:width 793,
:height 1121.5281146896566}),
:page 7},
:content {:text "행렬 A의 행은 전치 행렬 A의 열이다"},
:properties {:color "yellow"}}
{:id #uuid "6a68615c-4d21-4589-bb5e-a16ed5a59b1b",
:page 8,
:position {:bounding {:x1 248.0441297031939,
:y1 93.64059448242188,
:x2 591.983109805733,
:y2 116.46237182617188,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 248.0441297031939,
:y1 93.64059448242188,
:x2 591.983109805733,
:y2 116.46237182617188,
:width 793,
:height 1121.5281146896566}),
:page 8},
:content {:text "A의 행공간 은 전치행렬 A 의 열 공간 CAT ) 이다."},
:properties {:color "yellow"}}
{:id #uuid "6a6861d6-3ef8-4eb5-9a46-01cf243b0c8f",
:page 8,
:position {:bounding {:x1 171.91212591901422,
:y1 577.6523475646973,
:x2 205.01558050885797,
:y2 593.6275672912598,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 171.91212591901422,
:y1 577.6523475646973,
:x2 205.01558050885797,
:y2 593.6275672912598,
:width 793,
:height 1121.5281146896566}),
:page 8},
:content {:text "생성 "},
:properties {:color "yellow"}}
{:id #uuid "6a6861dd-f2db-430b-bc2a-4e46dfebc8c6",
:page 8,
:position {:bounding {:x1 123.22568640485406,
:y1 577.6523475646973,
:x2 727.206254336983,
:y2 652.0132484436035,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 664.2918866612017,
:y1 577.6523475646973,
:x2 724.626908633858,
:y2 593.6275672912598,
:width 793,
:height 1121.5281146896566}
{:x1 123.22568640485406,
:y1 608.1645545959473,
:x2 727.206254336983,
:y2 623.379093170166,
:width 793,
:height 1121.5281146896566}
{:x1 123.22568640485406,
:y1 637.559513092041,
:x2 638.2964642979205,
:y2 652.0132484436035,
:width 793,
:height 1121.5281146896566}),
:page 8},
:content {:text "S가 N개의 벡터 만 포함한다면, S는 확실히 부분공간 이 아니다 . 그러나 S의 모든 벡터 의 선형결합을 포함한다면 벡터공간 V 가 만들어진다. 이 경우 집합 S 는 벡터 공간 V를 생성한다 ."},
:properties {:color "yellow"}}
{:id #uuid "6a6861f6-3c80-4cbf-bb9a-c70b29f69418",
:page 9,
:position {:bounding {:x1 92.61835608258843,
:y1 242.956787109375,
:x2 691.678666446358,
:y2 289.6938781738281,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 92.61835608258843,
:y1 242.956787109375,
:x2 691.678666446358,
:y2 258.1712951660156,
:width 793,
:height 1121.5281146896566}
{:x1 112.20704779401422,
:y1 274.4793701171875,
:x2 290.56157049909234,
:y2 289.6938781738281,
:width 793,
:height 1121.5281146896566}),
:page 9},
:content {:text "Q. 언제 10개의 벡터 가 R' 을 생성 하는가? 이는 가능하다 . 그러나 아무렇게나 고른 10 개의 벡터로는 R ' 을 생성 할 수 없다 "},
:properties {:color "yellow"}}
{:id #uuid "6a6b5f7d-6107-49fa-8595-9e8cdea480e8",
:page 14,
:position {:bounding {:x1 121.64479956403375,
:y1 450.3020992279053,
:x2 719.552201602608,
:y2 495.1373348236084,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 392.1303571201861,
:y1 450.3020992279053,
:x2 719.552201602608,
:y2 465.5166072845459,
:width 793,
:height 1121.5281146896566}
{:x1 121.64479956403375,
:y1 479.9228572845459,
:x2 531.2131513096392,
:y2 495.1373348236084,
:width 793,
:height 1121.5281146896566}),
:page 14},
:content {:text "정사각행렬 A 가 가역행렬 (랭크는 = 2) 일 때, 유일한 해는 0이다 . 그러면 행렬 A 의 영공간은 영벡터 만 포함한다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b5f8a-654a-490b-862c-a5cb063f1188",
:page 15,
:position {:bounding {:x1 397.0512860752642,
:y1 293.2478942871094,
:x2 599.3797162510455,
:y2 314.5481872558594,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 397.0512860752642,
:y1 293.2478942871094,
:x2 599.3797162510455,
:y2 314.5481872558594,
:width 793,
:height 1121.5281146896566}),
:page 15},
:content {:text "특별해 S1 S2가 영공간 의 기저"},
:properties {:color "yellow"}}
{:id #uuid "6a6b5f99-2eb7-46ba-a875-32432525fbae",
:page 15,
:position {:bounding {:x1 98.72793707624078,
:y1 658.5388565063477,
:x2 675.8495038487017,
:y2 704.7648696899414,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 293.8364423252642,
:y1 658.5388565063477,
:x2 675.8495038487017,
:y2 672.9926528930664,
:width 793,
:height 1121.5281146896566}
{:x1 98.72793707624078,
:y1 687.2681655883789,
:x2 312.4341901279986,
:y2 704.7648696899414,
:width 793,
:height 1121.5281146896566}),
:page 15},
:content {:text "사다리꼴'이라는 용어는 1의 ' 계단 '을 의미한다 . 모든 영행은항상 RO 의 마지막 행에 위치 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b5fa3-a6fe-4467-9191-703689a8aceb",
:page 16,
:position {:bounding {:x1 126.95799383893609,
:y1 79.03225708007812,
:x2 730.6714032627642,
:y2 126.37557983398438,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 314.3342450596392,
:y1 79.03225708007812,
:x2 730.6714032627642,
:y2 95.00747680664062,
:width 793,
:height 1121.5281146896566}
{:x1 126.95799383893609,
:y1 108.87887573242188,
:x2 466.6382001377642,
:y2 126.37557983398438,
:width 793,
:height 1121.5281146896566}),
:page 16},
:content {:text "임의의 X\" 행렬 A로 시작 하여 소거법을 적용한다. 이에 따라행렬 A를 기약행 사다리꼴 Ro = rref ( A)로 바꾼다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b5fa9-754f-408e-8d16-bc39d56c1267",
:page 16,
:position {:bounding {:x1 126.95799383893609,
:y1 142.64797973632812,
:x2 729.6191571690142,
:y2 190.65689086914062,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 561.9148114658892,
:y1 142.64797973632812,
:x2 729.6191571690142,
:y2 158.62319946289062,
:width 793,
:height 1121.5281146896566}
{:x1 126.95799383893609,
:y1 176.20309448242188,
:x2 215.67944464460015,
:y2 190.65689086914062,
:width 793,
:height 1121.5281146896566}),
:page 16},
:content {:text "R의 모든 영행 을 제거하면 R 이 된다."},
:properties {:color "yellow"}}
{:id #uuid "6a6b5faf-d090-4dd6-8043-1d45e7583aa0",
:page 16,
:position {:bounding {:x1 427.18315253034234,
:y1 693.4371604919434,
:x2 664.9473432041705,
:y2 707.8909568786621,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 427.18315253034234,
:y1 693.4371604919434,
:x2 664.9473432041705,
:y2 707.8909568786621,
:width 793,
:height 1121.5281146896566}),
:page 16},
:content {:text "새로운 열 은 이전 열들과 선형종인가"},
:properties {:color "yellow"}}
{:id #uuid "6a6b5fc4-7bd5-41f6-b211-a7cfd1c1a282",
:page 17,
:position {:bounding {:x1 221.71589789167047,
:y1 960.2498168945312,
:x2 542.587601993233,
:y2 976.22509765625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 221.71589789167047,
:y1 960.2498168945312,
:x2 542.587601993233,
:y2 976.22509765625,
:width 793,
:height 1121.5281146896566}),
:page 17},
:content {:text "(A 의 선형 독립인 열) = (A의 선형종속인 열 ) X F"},
:properties {:color "red"}}
{:id #uuid "6a6b6003-baed-4e8c-8ee3-a2a1798181b3",
:page 19,
:position {:bounding {:x1 164.86352667585015,
:y1 525.3643188476562,
:x2 327.5811933018267,
:y2 541.3395385742188,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 164.86352667585015,
:y1 525.3643188476562,
:x2 327.5811933018267,
:y2 541.3395385742188,
:width 793,
:height 1121.5281146896566}),
:page 19},
:content {:text " A= CR과 영공간"},
:properties {:color "yellow"}}
{:id #uuid "6a6b6006-942c-4f60-ac32-9d2e8ad4e45a",
:page 19,
:position {:bounding {:x1 90.00336584821343,
:y1 619.611083984375,
:x2 687.7415936924517,
:y2 666.2412109375,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 632.4126752354205,
:y1 619.611083984375,
:x2 687.7415936924517,
:y2 634.8256225585938,
:width 793,
:height 1121.5281146896566}
{:x1 90.00336584821343,
:y1 651.0266723632812,
:x2 582.5031903721392,
:y2 666.2412109375,
:width 793,
:height 1121.5281146896566}),
:page 19},
:content {:text "RO 안에있는 는 행렬 A에서 선형 독립인 열들 로 이루어진 행렬 C의 위치를 알려준다."},
:properties {:color "yellow"}}
{:id #uuid "6a6b601a-66cb-4d23-a68d-5ef3b2fa7407",
:page 19,
:position {:bounding {:x1 110.61427435651422,
:y1 683.4526271820068,
:x2 393.26887640729547,
:y2 697.9064235687256,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 110.61427435651422,
:y1 683.4526271820068,
:x2 393.26887640729547,
:y2 697.9064235687256,
:width 793,
:height 1121.5281146896566}),
:page 19},
:content {:text "영행을 제거하면 A = CR 에서의 행 행렬 R"},
:properties {:color "yellow"}}
{:id #uuid "6a6b6080-45c0-4450-b783-ca74d3bbf525",
:page 21,
:position {:bounding {:x1 92.85608801618218,
:y1 180.9100799560547,
:x2 695.8328412510455,
:y2 257.4105682373047,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 93.96151861920953,
:y1 180.9100799560547,
:x2 695.8328412510455,
:y2 196.1245880126953,
:width 793,
:height 1121.5281146896566}
{:x1 93.96151861920953,
:y1 210.3050079345703,
:x2 692.5718549229205,
:y2 225.51951599121094,
:width 793,
:height 1121.5281146896566}
{:x1 92.85608801618218,
:y1 242.95677185058594,
:x2 511.69929632917047,
:y2 257.4105682373047,
:width 793,
:height 1121.5281146896566}),
:page 21},
:content {:text "원점만 있는 영 공간 Z는 굉장히 중요 하다. 이 경우 행렬 A의 열은 선형 독립이다 . 열들의 어떠한결합도 영벡터 를 만들지 않는다( 단, 0이 아닐 때 ). \"> 인 경우 에는 이런 상황이 발생하지않는다 . 다시 말해 R\" 에서 \"개의 선형 독립인 열을 가질 수 없다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b6086-5d0a-4dca-bbc9-4ee9dd539296",
:page 21,
:position {:bounding {:x1 92.85608801618218,
:y1 284.58274841308594,
:x2 692.5276654697955,
:y2 329.44175720214844,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 653.3802045322955,
:y1 284.58274841308594,
:x2 692.5276654697955,
:y2 299.79722595214844,
:width 793,
:height 1121.5281146896566}
{:x1 92.85608801618218,
:y1 314.98802185058594,
:x2 379.60847601667047,
:y2 329.44175720214844,
:width 793,
:height 1121.5281146896566}),
:page 21},
:content {:text ">m인 경우이므로 적어도 하나의 자유 변수가 있다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b609e-46ad-418b-aa3a-41a2cf13bf80",
:page 21,
:position {:bounding {:x1 196.5762799717486,
:y1 401.37791442871094,
:x2 514.977494571358,
:y2 415.8317108154297,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 196.5762799717486,
:y1 401.37791442871094,
:x2 514.977494571358,
:y2 415.8317108154297,
:width 793,
:height 1121.5281146896566}),
:page 21},
:content {:text "방정식보다 미지수의 개수 가 더 많다고 가정 하자"},
:properties {:color "yellow"}}
{:id #uuid "6a6b60a5-62e7-4143-ae8e-a9fcb1b8c238",
:page 21,
:position {:bounding {:x1 104.82563147321343,
:y1 430.99864196777344,
:x2 680.4747479893267,
:y2 473.8727264404297,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 104.82563147321343,
:y1 430.99864196777344,
:x2 680.4747479893267,
:y2 446.2131805419922,
:width 793,
:height 1121.5281146896566}
{:x1 104.82563147321343,
:y1 460.1796112060547,
:x2 121.199792239815,
:y2 473.8727264404297,
:width 793,
:height 1121.5281146896566}),
:page 21},
:content {:text "( n-2) 개의 자유변수가 있어야 한다 . Ar= 0 은 N (A ) 안에서 0이 아닌 해 를 가져야 한다."},
:properties {:color "yellow"}}
{:id #uuid "6a6b60b0-448f-44b1-b8b9-cd7dce5bda13",
:page 22,
:position {:bounding {:x1 121.00293860211968,
:y1 638.0111923217773,
:x2 724.571000430733,
:y2 683.7735824584961,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 548.197953555733,
:y1 638.0111923217773,
:x2 724.571000430733,
:y2 655.5078353881836,
:width 793,
:height 1121.5281146896566}
{:x1 121.00293860211968,
:y1 669.3197860717773,
:x2 488.5302899815142,
:y2 683.7735824584961,
:width 793,
:height 1121.5281146896566}),
:page 22},
:content {:text "블록 소거법 ( block elimination)을 설명 할 수 있다 . 이때 행렬 A의 랭크 는 ' 로 가정 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b60bd-44b4-4ea0-aaff-fdf73e00e3e4",
:page 22,
:position {:bounding {:x1 173.57621893659234,
:y1 710.3752059936523,
:x2 429.37642035260797,
:y2 727.8719100952148,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 173.57621893659234,
:y1 710.3752059936523,
:x2 429.37642035260797,
:y2 727.8719100952148,
:width 793,
:height 1121.5281146896566}),
:page 22},
:content {:text "PC를 이용해 행렬 A 의 열의 위치를 바꾼다"},
:properties {:color "yellow"}}
{:id #uuid "6a6b60c4-122e-4a43-a498-869cda9a821d",
:page 22,
:position {:bounding {:x1 395.9339765049517,
:y1 829.7616195678711,
:x2 619.0999921299517,
:y2 847.2582626342773,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 395.9339765049517,
:y1 829.7616195678711,
:x2 619.0999921299517,
:y2 847.2582626342773,
:width 793,
:height 1121.5281146896566}),
:page 22},
:content {:text "W- 1B = [ IW-H ][IF]"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8b64-26a8-43aa-9932-df6a352d35e0",
:page 29,
:position {:bounding {:x1 91.26331457868218,
:y1 488.21951808035374,
:x2 692.367387149483,
:y2 564.3871511369944,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 357.3984540440142,
:y1 488.21951808035374,
:x2 692.367387149483,
:y2 503.43402613699436,
:width 793,
:height 1121.5281146896566}
{:x1 92.2974256016314,
:y1 519.7539724260569,
:x2 691.2619794346392,
:y2 534.9685110002756,
:width 793,
:height 1121.5281146896566}
{:x1 91.26331457868218,
:y1 549.9334157854319,
:x2 440.5048993565142,
:y2 564.3871511369944,
:width 793,
:height 1121.5281146896566}),
:page 29},
:content {:text "소거 를 통해 Az =0 에 대한 문제는 Ro =0 으로 변환되었다 . 자유변수 에는 특별한 값 (1 과 0) 이 주어졌다 . 그런 다음 역대 입법을 통해 피벗 변수를구했다. 우변 b 는 0이었으므로 주의 를 기울이지 않았다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8b6a-74ce-4dfa-a873-9dc8a8ff9731",
:page 29,
:position {:bounding {:x1 91.26331457868218,
:y1 623.7594655901194,
:x2 690.848588321358,
:y2 700.9968923479319,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 524.6392377354205,
:y1 623.7594655901194,
:x2 690.848588321358,
:y2 638.2132619768381,
:width 793,
:height 1121.5281146896566}
{:x1 91.26331457868218,
:y1 653.2731985002756,
:x2 689.110551211983,
:y2 668.4877370744944,
:width 793,
:height 1121.5281146896566}
{:x1 91.26331457868218,
:y1 685.0216115862131,
:x2 175.13333258405328,
:y2 700.9968923479319,
:width 793,
:height 1121.5281146896566}),
:page 29},
:content {:text "Ar = b는 동일한 해 ( 해가존재할 경우 ) 를 가진 더 간단한 연립방정식 Ror= d 로 축소된다. 이제 벡터 6 를 행렬 A의 열로 추가하자 "},
:properties {:color "yellow"}}
{:id #uuid "6a6c8d7a-b23c-4b70-9165-038a57e92b21",
:page 30,
:position {:bounding {:x1 231.54589972272515,
:y1 554.6522674560547,
:x2 555.3958905674517,
:y2 570.6274871826172,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 231.54589972272515,
:y1 554.6522674560547,
:x2 555.3958905674517,
:y2 570.6274871826172,
:width 793,
:height 1121.5281146896566}),
:page 30},
:content {:text "가장 간단한 해 는 자유 변수를 0으로 선택한 경우이다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8d82-54da-4741-acfc-d0436c06b871",
:page 30,
:position {:bounding {:x1 182.2294782139361,
:y1 653.9388885498047,
:x2 486.9359296299517,
:y2 668.3926239013672,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 182.2294782139361,
:y1 653.9388885498047,
:x2 486.9359296299517,
:y2 668.3926239013672,
:width 793,
:height 1121.5281146896566}),
:page 30},
:content {:text "자유변수 는 0이고, 피벗변수는 d로부터 구한다."},
:properties {:color "yellow"}}
{:id #uuid "6a6c8d91-bd90-4bce-82d5-5c0f3e107286",
:page 30,
:position {:bounding {:x1 127.43345007672906,
:y1 696.9198455810547,
:x2 641.4383710362017,
:y2 712.1343841552734,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 127.43345007672906,
:y1 696.9198455810547,
:x2 641.4383710362017,
:y2 712.1343841552734,
:width 793,
:height 1121.5281146896566}),
:page 30},
:content {:text "해가 존재 하려면 R의 영향이 있는 위치와 동일한 d 의 위치에도 0 이 있어야 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8d95-71f7-4bb7-9776-f2902bd07ed2",
:page 30,
:position {:bounding {:x1 127.43345007672906,
:y1 859.0495357513428,
:x2 628.9004071690142,
:y2 874.2640743255615,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 127.43345007672906,
:y1 859.0495357513428,
:x2 628.9004071690142,
:y2 874.2640743255615,
:width 793,
:height 1121.5281146896566}),
:page 30},
:content {:text "자유변수에 0 을 할당 한 다음, 피벗 변수를 푸는 방법을 사용한다는 점에 주목하자"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8e62-e01d-4ebd-9cd8-23ae3100bd71",
:page 31,
:position {:bounding {:x1 83,
:y1 425.63671875,
:x2 699,
:y2 562.63671875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 31},
:content {:text "[:span]", :image 1785499234632},
:properties {:color "yellow"}}
{:id #uuid "6a6c8f97-0501-4709-b253-74ce2701c214",
:page 32,
:position {:bounding {:x1 322.5833600498736,
:y1 337.4294128417969,
:x2 712.4839642979205,
:y2 352.6439514160156,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 322.5833600498736,
:y1 337.4294128417969,
:x2 712.4839642979205,
:y2 352.6439514160156,
:width 793,
:height 1121.5281146896566}),
:page 32},
:content {:text "자유변수가 없다 . 따라서 Ar=b 의 0 이 아닌 특별 해가 없다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8f9d-cfdb-4ec3-bb34-871a9d30fc43",
:page 32,
:position {:bounding {:x1 157.16117987409234,
:y1 365.9328308105469,
:x2 434.31755194440484,
:y2 381.1473693847656,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 157.16117987409234,
:y1 365.9328308105469,
:x2 434.31755194440484,
:y2 381.1473693847656,
:width 793,
:height 1121.5281146896566}),
:page 32},
:content {:text "행렬 A 의 영 공간 안에는 = 0 밖에 없다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8fad-831a-4c79-8c57-7e8812379132",
:page 32,
:position {:bounding {:x1 137.50117621198297,
:y1 365.9328308105469,
:x2 716.1876386143267,
:y2 412.0162048339844,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 448.5191510654986,
:y1 365.9328308105469,
:x2 716.1876386143267,
:y2 381.1473693847656,
:width 793,
:height 1121.5281146896566}
{:x1 137.50117621198297,
:y1 397.5624084472656,
:x2 255.20718512311578,
:y2 412.0162048339844,
:width 793,
:height 1121.5281146896566}),
:page 32},
:content {:text "Az = b와 Rod 의 특수 해는 최종 열 d 의 맨 위에 있다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8fb4-b4c8-4733-8267-cfda78c4cebb",
:page 32,
:position {:bounding {:x1 173.65942511335015,
:y1 492.1538848876953,
:x2 579.9295209385455,
:y2 508.12913513183594,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 173.65942511335015,
:y1 492.1538848876953,
:x2 579.9295209385455,
:y2 508.12913513183594,
:width 793,
:height 1121.5281146896566}),
:page 32},
:content {:text "b3+6, +b2가 0 이 아니라면, Ax=b 의 해는 존재 하지 않는다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c8fda-58b7-4864-ae16-7bb588894775",
:page 32,
:position {:bounding {:x1 111,
:y1 808.78515625,
:x2 732,
:y2 972.78515625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 32},
:content {:text "[:span]", :image 1785499609883},
:properties {:color "yellow"}}
{:id #uuid "6a6c90ae-d786-4d85-b619-34886a39c665",
:page 33,
:position {:bounding {:x1 87.138757083565,
:y1 401.37792587280273,
:x2 689.483598086983,
:y2 449.17287826538086,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 562.027055118233,
:y1 401.37792587280273,
:x2 689.483598086983,
:y2 419.6353416442871,
:width 793,
:height 1121.5281146896566}
{:x1 87.138757083565,
:y1 431.6762046813965,
:x2 616.5293134190142,
:y2 449.17287826538086,
:width 793,
:height 1121.5281146896566}),
:page 33},
:content {:text "r =m 인 경우 행렬 A는 최대 행 랭크 를 갖는다 . 이때 ' 행은 선형 독립이다 . 모든 행 에는 피벗 이 있다."},
:properties {:color "yellow"}}
{:id #uuid "6a6c90cf-8d1d-49e5-a86a-24b1367c0ae2",
:page 33,
:position {:bounding {:x1 98.0028699375689,
:y1 620.0627899169922,
:x2 675.3401044346392,
:y2 664.4463653564453,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 347.4852460362017,
:y1 620.0627899169922,
:x2 675.3401044346392,
:y2 636.0380401611328,
:width 793,
:height 1121.5281146896566}
{:x1 98.0028699375689,
:y1 649.2318572998047,
:x2 519.0683759190142,
:y2 664.4463653564453,
:width 793,
:height 1121.5281146896566}),
:page 33},
:content {:text "특수해 는 이 직선 위 의 한 점이 될 것이다. 영 공간벡터 1을 더하면 [ 그림 3.1] 과 같이 직선 을 따라 이동할 수 있다"},
:properties {:color "yellow"}}
{:id #uuid "6a6c9114-fac6-42ae-8391-2cc98b17b69f",
:page 34,
:position {:bounding {:x1 130,
:y1 510.46875,
:x2 736,
:y2 721.46875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 34},
:content {:text "[:span]", :image 1785499924061},
:properties {:color "yellow"}}
{:id #uuid "6a6c9135-9a2d-4d8c-bc9c-f44beb7b6a9c",
:page 35,
:position {:bounding {:x1 56,
:y1 140.07421875,
:x2 712,
:y2 251.07421875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 35},
:content {:text "[:span]", :image 1785499957027},
:properties {:color "yellow"}}
{:id #uuid "6a6c91c8-cec5-4d43-a8f1-c4f9cf27cc20",
:page 35,
:position {:bounding {:x1 181.19535956159234,
:y1 529.5126647949219,
:x2 473.5351422764361,
:y2 544.7272033691406,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 181.19535956159234,
:y1 529.5126647949219,
:x2 473.5351422764361,
:y2 544.7272033691406,
:width 793,
:height 1121.5281146896566}),
:page 35},
:content {:text "랜덤 선형 대수학(randomized linear algebra) 이다"},
:properties {:color "yellow"}}
{:id #uuid "6a6e8c06-7997-4313-a309-d5b6e1814f20",
:page 38,
:position {:bounding {:x1 100,
:y1 325.140625,
:x2 730,
:y2 481.140625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 38},
:content {:text "[:span]", :image 1785629702028},
:properties {:color "yellow"}}
{:id #uuid "6a6e8c0f-85fc-456f-9dae-c8a4bdbed593",
:page 38,
:position {:bounding {:x1 109,
:y1 495.140625,
:x2 726,
:y2 643.140625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 38},
:content {:text "[:span]", :image 1785629711418},
:properties {:color "yellow"}}
{:id #uuid "6a6e8c28-2ec2-4994-a90e-16eeb55f3995",
:page 23,
:position {:bounding {:x1 77,
:y1 845.1796875,
:x2 631,
:y2 895.1796875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 23},
:content {:text "[:span]", :image 1785629736506},
:properties {:color "yellow"}}
{:id #uuid "6a6e8c2e-7386-47f6-ba4d-c76b8aced7a6",
:page 23,
:position {:bounding {:x1 82,
:y1 904.1796875,
:x2 715,
:y2 1029.1796875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 23},
:content {:text "[:span]", :image 1785629741990},
:properties {:color "yellow"}}
{:id #uuid "6a6e8ca7-0b52-401e-bd74-5dcf2b17cb3a",
:page 10,
:position {:bounding {:x1 120,
:y1 776.8916015625,
:x2 738,
:y2 928.8916015625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 10},
:content {:text "[:span]", :image 1785629862792},
:properties {:color "yellow"}}
{:id #uuid "6a6e8cb1-133b-4204-8a09-47f562a1fa03",
:page 11,
:position {:bounding {:x1 65,
:y1 58.2607421875,
:x2 592,
:y2 291.2607421875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 11},
:content {:text "[:span]", :image 1785629873392},
:properties {:color "yellow"}}
{:id #uuid "6a6e8cb5-cc8c-4021-9e2b-46343aac3aff",
:page 11,
:position {:bounding {:x1 71,
:y1 302.2607421875,
:x2 647,
:y2 372.2607421875,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 11},
:content {:text "[:span]", :image 1785629877623},
:properties {:color "yellow"}}
{:id #uuid "6a6f4c69-edda-46af-a200-d4fef344636e",
:page 42,
:position {:bounding {:x1 116.48613104596734,
:y1 933.3272705078125,
:x2 715.956742618233,
:y2 976.2726440429688,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 495.6960309483111,
:y1 933.3272705078125,
:x2 715.956742618233,
:y2 947.7810668945312,
:width 793,
:height 1121.5281146896566}
{:x1 116.48613104596734,
:y1 961.81884765625,
:x2 206.3035291172564,
:y2 976.2726440429688,
:width 793,
:height 1121.5281146896566}),
:page 42},
:content {:text "열공간 C( A)의 차원은 선형독립인열의 개수이다"},
:properties {:color "yellow"}}
{:id #uuid "6a6f4c77-478f-4e0c-95f3-672a664d0a48",
:page 42,
:position {:bounding {:x1 307.20243963971734,
:y1 961.81884765625,
:x2 464.1496747471392,
:y2 976.2726440429688,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 307.20243963971734,
:y1 961.81884765625,
:x2 464.1496747471392,
:y2 976.2726440429688,
:width 793,
:height 1121.5281146896566}),
:page 42},
:content {:text "열공간의 차원이 랭크' "},
:properties {:color "yellow"}}
{:id #uuid "6a6f4c82-32f3-4bb0-a532-e3caa323b520",
:page 43,
:position {:bounding {:x1 95.31656012311578,
:y1 183.94110107421875,
:x2 694.0908978916705,
:y2 229.1329345703125,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 628.680375430733,
:y1 183.94110107421875,
:x2 694.0908978916705,
:y2 198.3948974609375,
:width 793,
:height 1121.5281146896566}
{:x1 95.31656012311578,
:y1 214.67913818359375,
:x2 404.9913495518267,
:y2 229.1329345703125,
:width 793,
:height 1121.5281146896566}),
:page 43},
:content {:text "벡터공간의모든 벡터는 기저 벡터 들의 유일한 선형 결합 이다 ."},
:properties {:color "yellow"}}
{:id #uuid "6a6f4cdf-c66d-4a98-8845-78fbb19ad2e4",
:page 44,
:position {:bounding {:x1 124.17659125104547,
:y1 980.7775573730469,
:x2 373.6827558018267,
:y2 996.7527770996094,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 124.17659125104547,
:y1 980.7775573730469,
:x2 373.6827558018267,
:y2 996.7527770996094,
:width 793,
:height 1121.5281146896566}),
:page 44},
:content {:text "R'에서 세 벡터 는 선형 독립 일 수 없다. "},
:properties {:color "yellow"}}
{:id #uuid "6a6f4ce8-31ef-4a06-a0fb-ab832885cd01",
:page 44,
:position {:bounding {:x1 124.17659125104547,
:y1 980.7775573730469,
:x2 719.2234662510455,
:y2 1026.5162048339844,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 591.0125897862017,
:y1 980.7775573730469,
:x2 719.2234662510455,
:y2 996.7527770996094,
:width 793,
:height 1121.5281146896566}
{:x1 124.17659125104547,
:y1 1011.3016662597656,
:x2 638.1815350987017,
:y2 1026.5162048339844,
:width 793,
:height 1121.5281146896566}),
:page 44},
:content {:text "세 벡터를 열로 갖는행렬 A 는 자유 변수를 가져야 하고 , Ar=0 에 대해 0이 아닌 해를 가져야 한다"},
:properties {:color "yellow"}}
{:id #uuid "6a6f4d91-d89b-4163-b894-a262f88ce1f5",
:page 45,
:position {:bounding {:x1 71,
:y1 501.7890625,
:x2 702,
:y2 587.7890625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 45},
:content {:text "[:span]", :image 1785679249138},
:properties {:color "yellow"}}
{:id #uuid "6a6f4e1c-c4c1-4bfa-a925-8e0125831521",
:page 45,
:position {:bounding {:x1 83,
:y1 756.7890625,
:x2 698,
:y2 815.7890625,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 45},
:content {:text "[:span]", :image 1785679388176},
:properties {:color "yellow"}}
{:id #uuid "6a6f4e82-c6f4-478d-a115-03f4ad48968d",
:page 46,
:position {:bounding {:x1 260.18010077252984,
:y1 897.4186401367188,
:x2 592.0054486729205,
:y2 912.6331787109375,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 260.18010077252984,
:y1 897.4186401367188,
:x2 592.0054486729205,
:y2 912.6331787109375,
:width 793,
:height 1121.5281146896566}),
:page 46},
:content {:text "기저벡터 는 선형 독립 이며, 벡터 공간 전체를 생성 한다."},
:properties {:color "yellow"}}
{:id #uuid "6a6f4ebe-80ba-445c-8928-36a513c94dc1",
:page 47,
:position {:bounding {:x1 191.58401617780328,
:y1 76.1201171875,
:x2 590.4784100987017,
:y2 94.37750244140625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 191.58401617780328,
:y1 76.1201171875,
:x2 590.4784100987017,
:y2 94.37750244140625,
:width 793,
:height 1121.5281146896566}),
:page 47},
:content {:text "벡터 \"를 기저벡터의 선형 결합 으로 나타내는 방법 은 유일하다."},
:properties {:color "yellow"}}
{:id #uuid "6a6f4f88-b220-4eb1-be8d-9877258f5b02",
:page 47,
:position {:bounding {:x1 210.13859686627984,
:y1 936.1324310302734,
:x2 560.8979657627642,
:y2 977.1284027099609,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 210.13859686627984,
:y1 936.1324310302734,
:x2 560.8979657627642,
:y2 953.6291351318359,
:width 793,
:height 1121.5281146896566}
{:x1 216.72363409772515,
:y1 961.1531829833984,
:x2 554.3204511143267,
:y2 977.1284027099609,
:width 793,
:height 1121.5281146896566}),
:page 47},
:content {:text "선형독립 인 벡터 의 모든 집합은 기저 로 확장될 수 있다.생성 하는 벡터 의 모든 집합은 기저 로 축소될 수 있다."},
:properties {:color "yellow"}}
{:id #uuid "6a6f4fca-2af6-43da-827e-92bd8b2c6820",
:page 48,
:position {:bounding {:x1 226.0781873203814,
:y1 829.3098983764648,
:x2 620.3718427158892,
:y2 843.7636947631836,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 226.0781873203814,
:y1 829.3098983764648,
:x2 620.3718427158892,
:y2 843.7636947631836,
:width 793,
:height 1121.5281146896566}),
:page 48},
:content {:text "모든 기저에 있는 벡터의 개수를 벡터공간의 ' 차원 ' 이라 한다 "},
:properties {:color "yellow"}}
{:id #uuid "6a6f5076-d814-467f-803d-480ea4bd521b",
:page 49,
:position {:bounding {:x1 143.3730329014361,
:y1 96.4219970703125,
:x2 652.9998334385455,
:y2 117.7222900390625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 143.3730329014361,
:y1 96.4219970703125,
:x2 652.9998334385455,
:y2 117.7222900390625,
:width 793,
:height 1121.5281146896566}),
:page 49},
:content {:text "01,... , Um 과 201, ... , W , 이 동일한 벡터 공간의 기저 벡터 일 때 , m = \" 이다 "},
:properties {:color "yellow"}}
{:id #uuid "6a6f5096-4c95-4cb3-85f9-00801a8c0ee6",
:page 50,
:position {:bounding {:x1 238,
:y1 170.75,
:x2 620,
:y2 242.75,
:width 793,
:height 1121.5281146896566},
:rects (),
:page 50},
:content {:text "[:span]", :image 1785680022562},
:properties {:color "yellow"}}
{:id #uuid "6a6f51df-be99-4490-af36-c4321ee42a5f",
:page 50,
:position {:bounding {:x1 130.3574841953814,
:y1 278.63958740234375,
:x2 344.9999860264361,
:y2 296.13629150390625,
:width 793,
:height 1121.5281146896566},
:rects ({:x1 130.3574841953814,
:y1 278.63958740234375,
:x2 344.9999860264361,
:y2 296.13629150390625,
:width 793,
:height 1121.5281146896566}),
:page 50},
:content {:text "행렬 공간과 함수 공간 의 기저"},
:properties {:color "yellow"}}
{:id #uuid "6a721cb1-5e66-4c0c-a427-5b12c011775f",
:page 29,
:position {:bounding {:x1 97,
:y1 180,
:x2 879,
:y2 574,
:width 992.1266666666666,
:height 1403.1499999999999},
:rects (),
:page 29},
:content {:text "[:span]", :image 1785863342916},
:properties {:color "yellow"}}
{:id #uuid "6a721cde-db1e-4292-8c42-8a16bdccb176",
:page 34,
:position {:bounding {:x1 148,
:y1 1057,
:x2 909,
:y2 1225,
:width 992.1266666666666,
:height 1403.1499999999999},
:rects (),
:page 34},
:content {:text "[:span]", :image 1785863387860},
:properties {:color "yellow"}}
{:id #uuid "6a721cf3-66c1-4999-bb96-619ea9fc3774",
:page 42,
:position {:bounding {:x1 127,
:y1 859,
:x2 901,
:y2 1098,
:width 992.1266666666666,
:height 1403.1499999999999},
:rects (),
:page 42},
:content {:text "[:span]", :image 1785863409283},
:properties {:color "yellow"}}
{:id #uuid "6a721d15-4d6e-4878-8085-4ac8ae3ae6a0",
:page 60,
:position {:bounding {:x1 124,
:y1 175,
:x2 914,
:y2 427,
:width 992.1266666666666,
:height 1403.1499999999999},
:rects (),
:page 60},
:content {:text "[:span]", :image 1785863444248},
:properties {:color "yellow"}}
{:id #uuid "6a721d23-54c9-4769-849c-79f5b9355467",
:page 65,
:position {:bounding {:x1 81,
:y1 179,
:x2 891,
:y2 332,
:width 992.1266666666666,
:height 1403.1499999999999},
:rects (),
:page 65},
:content {:text "[:span]", :image 1785863457636},
:properties {:color "yellow"}}],
:extra {:page 25}}
Reference in New Issue View Git Blame Copy Permalink