И.С. Ломов - Алгебра и геометрия (1108716), страница 3
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Ðàäèóñ-âåêòîð òî÷êèÀ: 13.1, 17, 3, 4, 9, 16, 22, 34, 29Ä: 13.2, 5, 7, 8, 10, 14, 16.1, 16.2, 23, 33, 35, 37Ð: 13.42, 45, 46Ñåìèíàð 9Ëèíåéíîå ïðîñòðàíñòâîÀêñèîìû ëèíåéíîãî ïðîñòðàíñòâà. Ïðèìåðû. Àðèôìåòè÷åñêîå ïðîñòðàíñòâî. Ëèíåéíàÿ çàâèñèìîñòüÀ: 14.1, 5, 7, 8, 15.1, 4, 68, 11, 17, 25, 29Ä: 14.24, 6, 9, 15.2, 3, 5, 12, 20, 21, 23, 24, 26, 30Ð: 14.1012, 15.35, 3615Àëãåáðà è ãåîìåòðèÿÑåìèíàð 10Ðàíã ìàòðèöû1. Ðàíã ìàòðèöû è ýëåìåíòàðíûå ïðåîáðàçîâàíèÿ å¼ñòðîê è ñòîëáöîâ. Ìåòîä Ãàóññà âû÷èñëåíèÿ ðàíãàÀ: 16.1, 5, 10, 15, 17, 18, 20, 24, 3436Ä: 16.2, 3, 7, 11, 13, 19, 23, 28Ð: 16.20.1, 30, 33Ñåìèíàð 112.
Ðàíã ìàòðèöû è ëèíåéíàÿ çàâèñèìîñòü å¼ ñòðîê èñòîëáöîâÀ: 16.38, 39, 42, 55Ä: 16.37, 40, 41, 43, 60, 61Ñèñòåìû ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèé1. Ïðàâèëî ÊðàìåðàÀ: 19.3, 10, 17, 26Ä: 19.2, 8, 11, 19Ð: 16.42.1, 44, 44.1, 47, 51, 52, 63, 64, 19.1215, 25Ñåìèíàð 122.
Êðèòåðèé ñîâìåñòíîñòè ñèñòåì îáùåãî âèäàÀ: 20.1, 3, 5, 7, 21.57Ä: 20.2, 4, 6, 8, 21.55, 593. Ìåòîä Ãàóññà èññëåäîâàíèÿ è ðåøåíèÿ ñèñòåì. Îáùåå ðåøåíèåÀ: 21.13, 46(á), 26, 35, 52Ä: 21.4, 5, 12, 17, 46(à), 47, 53, 27, 33, 48(à), 35Ð: 20.8, 9, 11, 21.58, 60, 62Ñåìèíàð 13Ãåîìåòðè÷åñêèå ñâîéñòâà ìíîæåñòâà ðåøåíèé ñèñòåìû1. Ëèíåéíîå ïîäïðîñòðàíñòâî ðåøåíèé îäíîðîäíîéñèñòåìû óðàâíåíèé.
Ôóíäàìåíòàëüíàÿ ñèñòåìà ðåøåíèé. Îáùåå ðåøåíèå16Ñåìèíàðñêèå çàíÿòèÿÀ: 22.1, 2, 4, 10, 14, 15Ä: 22.3, 9, 12, 162. Ëèíåéíîå ìíîãîîáðàçèå ðåøåíèé íåîäíîðîäíîéñèñòåìû. Îáùåå ðåøåíèåÀ: 22.20, 26, 30, 33, 35, 3840Ä: 22.21, 27, 28, 32, 34, 48Ð: 22.29, 37, 41, 46, 49, 50Ñåìèíàð 14Êîëëîêâèóì (ñì. ñòð. 30)Ñåìèíàð 15Êîíòðîëüíàÿ ðàáîòà 1 (ñì. ñòð. 34)Òåìû: ìàòðè÷íàÿ àëãåáðà, îïðåäåëèòåëè, ðàíã ìàòðèöû, îáðàòíàÿìàòðèöà, ñèñòåìû ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèéÑåìèíàð 16Àôôèííàÿ è ïðÿìîóãîëüíàÿ äåêàðòîâà ñèñòåìû êîîðäèíàò1. Êîîðäèíàòû òî÷êèÀ: 23.1, 3, 5Ä: 23.2, 6, 7, 92. Äåëåíèå îòðåçêà â äàííîì îòíîøåíèèÀ: 23.19, 14, 26, 33Ä: 23.20, 17, 22, 29, 34, 353.
Ïðåîáðàçîâàíèå êîîðäèíàòÀ: 23.39, 43, 48, 62, 63, 56, 67Ä: 23.38, 47, 49, 51, 53, 57, 64, 66Ð: 23.55, 65, 65.1Ñåìèíàð 17Ñêàëÿðíîå ïðîèçâåäåíèåÀ: 24.4, 6, 8, 12, 15, 20, 27, 32, 47, 58, 67, 75, 78Ä: 24.5, 7, 13, 16, 17, 26, 28, 34, 36, 48, 49, 57, 63, 69, 74, 79Ð: 24.33, 34.1, 34.2, 3941, 73, 76, 78, 87, 90, 9117Àëãåáðà è ãåîìåòðèÿÑåìèíàð 18Âåêòîðíîå è ñìåøàííîå ïðîèçâåäåíèÿÀ: 25.5, 7, 11, 14, 22, 26, 35, 37, 44, 49, 59, 62Ä: 25.4, 6, 8, 9, 16, 17, 25, 27, 33, 36, 38, 40, 46, 48, 52, 64, 65, 71Ð: 25.20, 12, 63, 66, 67, 72, 74, 75Ñåìèíàð 19Ïðÿìàÿ íà ïëîñêîñòèÀ:Ä:À:Ä:À:Ä:Ð:1. Ñïîñîáû çàäàíèÿ26.7, 18, 2126.8, 10, 15, 19, 20, 22, 242. Âçàèìíîå ðàñïîëîæåíèå ïðÿìûõ27.8, 15, 20, 2527.10, 13, 16, 22, 243. Ïîëóïëîñêîñòè28.4, 11, 2028.6, 9, 1326.27, 27.26, 28Ñåìèíàð 204.
Ìåòðè÷åñêèå çàäà÷èÀ: 29.1, 6, 18, 33, 37, 44(1), 45(1), 56Ä: 29.35, 9, 35, 38, 43, 44(2), 45(2), 55, 57, 78Ïëîñêîñòü â ïðîñòðàíñòâå1. Ñïîñîáû çàäàíèÿÀ: 26.31, 39, 44Ä: 26.29, 32, 34, 38, 50Ð: 29.39, 6518Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 21À:Ä:À:Ä:À:Ä:Ð:2. Âçàèìíîå ðàñïîëîæåíèå ïëîñêîñòåé27.37, 4027.35, 33, 39, 493. Ïîëóïðîñòðàíñòâà28.2028.17, 184. Ìåòðè÷åñêèå çàäà÷è29.79, 8829.81, 83, 89, 93, 10227.53, 54, 28.19, 21, 23, 29.91, 92Ñåìèíàð 22Ïðÿìàÿ â ïðîñòðàíñòâåÀ:Ä:À:Ä:Ð:1. Ñïîñîáû çàäàíèÿ. Ðàñïîëîæåíèå ïðÿìûõ â ïðîñòðàíñòâå31.2(1), 4(1), 11(2), 13, 18(1,2), 2331.1, 2(2), 3, 4(2), 5, 11(1), 14, 15, 18(3,4), 19, 24, 31, 342. Ìåòðè÷åñêèå çàäà÷è32.3, 5, 8, 13, 20, 34, 3932.10, 17, 21, 26, 36, 37, 3832.32.1, 31.36, 32.40, 42Ñåìèíàð 23Âåêòîðíûå óðàâíåíèÿ ïðÿìîé è ïëîñêîñòèÀ: 33.5, 8, 10, 15, 20, 26, 29, 35, 41Ä: 33.6, 7, 11, 12, 22, 23, 27, 30, 36, 40Ð: 33.1, 31, 33, 41, 42, 44Ñåìèíàð 24Êîíòðîëüíàÿ ðàáîòà 2 (ñì.
ñòð. 35)Òåìû: äåëåíèå îòðåçêà â îòíîøåíèè, ïðåîáðàçîâàíèå êîîðäèíàò,ñêàëÿðíîå, âåêòîðíîå è ñìåøàííîå ïðîèçâåäåíèÿ, ïðÿìàÿ íàïëîñêîñòè, ïëîñêîñòü â ïðîñòðàíñòâå, ïðÿìàÿ â ïðîñòðàíñòâå19Àëãåáðà è ãåîìåòðèÿÑåìèíàð 25Ýëåìåíòû îáùåé àëãåáðûÀ:Ä:À:Ä:Ð:1. Ãðóïïà. Ïðèìåðû ãðóïï. Ïðîñòåéøèå ñâîéñòâà39.1(18), 2(18), 3(15), 4(1,2), 8, 1039.1(917), 2(918), 3(613), 4(35), 5, 92.
Èçîìîðôèçì ãðóïï39.11, 13, 14, 17, 2039.12, 16, 19, 21, 2439.23Ñåìèíàð 26À:Ä:À:Ä:Ð:3. Ïîäãðóïïà. Ñìåæíûå êëàññû, íîðìàëüíûé äåëèòåëü. Ôàêòîð-ãðóïïà39.25, 26, 28(à), 30, 38, 44(àâ), 45, 47, 82(à,á), 84(à)39.27, 29, 31, 32, 40, 44(ã,ä), 46, 48, 82(â,ã), 84(á,â)4. Ïîðÿäîê ýëåìåíòà. Öèêëè÷åñêèå ãðóïïû39.53(à,á), 54(à), 5658, 28(á), 61, 6439.53(â,ä), 54(á), 59, 60, 65, 7239.83, 55Ñåìèíàð 275. Êîëüöî è ïîëåÀ: 40.14, 8, 10, 11, 26, 27, 33, 38Ä: 40.14, 8, 12, 13, 15, 30, 32, 39Ð: 40.40, 47, 48, 54, 56, 58Ñåìèíàð 28Êîìïëåêñíûå ÷èñëà1. Ïîëå êîìïëåêñíûõ ÷èñåëÀ: 41.1(à,ã,å), 5(à), 6(à), 7, 9(à), 10(â,ã), 11(à), 15Ä: 41.1, 5, 6(á), 8, 9(á), 10(á,ä,å), 11, 16, 21Ð: 41.13, 2320Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 29À:Ä:À:Ä:Ð:2.
Òðèãîíîìåòðè÷åñêàÿ ôîðìà çàïèñè êîìïëåêñíîãî÷èñëà. Ôîðìóëà Ìóàâðà42.13, 8, 23(à), 27, 3242.1, 3, 5, 6, 9, 10, 23(á), 28, 31(à,á)3. Èçâëå÷åíèå êîðíÿ43.2, 6, 7, 11, 15(à,â), 20, 2543.13, 5, 8, 9, 1417, 21, 23, 24, 2742.19, 21, 21.1, 43.29, 32, 32.1Ñåìèíàð 30Ëèíèè âòîðîãî ïîðÿäêà íà ïëîñêîñòè1. Ýëëèïñ, ãèïåðáîëà, ïàðàáîëàÀ: 34.1, 6, 13, 18, 20, 26, 32, 36, 40, 49, 61, 66Ä: 34.1, 4, 9, 11, 13, 16, 2224, 29, 39, 44, 58, 64, 65Ð: 34.9(15), 10(2,3), 21(1,37), 36(1,2), 45, 50(1,2), 53, 55(1,2)Ñåìèíàð 312. Ëèíèè, çàäàííûå îáùèì óðàâíåíèåìÀ: 35.5, 11, 14, 19, 22, 23(1), 24(4), 27(1)Ä: 35.6, 10, 2022, 23(24), 24, 27Ð: 35.7, 9.1, 17, 26, 28Ñåìèíàð 32Ïîâåðõíîñòè âòîðîãî ïîðÿäêà1. Ýëëèïñîèä, ãèïåðáîëîèäû, ïàðàáîëîèäûÀ: 36.1, 5, 8(1), 13(1), 17, 18, 33, 40, 46Ä: 36.3, 6, 8(2), 13(2,3), 19, 20, 23, 32, 36, 47, 522.
Êîíóñû, öèëèíäðûÀ: 37.1, 6, 8, 16Ä: 37.2, 5, 7, 15, 193. Ïîâåðõíîñòè, çàäàííûå îáùèì óðàâíåíèåìÀ: 38.1, 9(1,2), 10, 11(1,2), 12(2)Ä: 38.4, 6(1), 712Ð: 36.1114, 25, 31, 33.1, 4344.1, 51, 53, 37.18, 21, 22, 38.221Àëãåáðà è ãåîìåòðèÿÏëàí ñåìèíàðñêèõ çàíÿòèé, 2 ñåìåñòðÑåìèíàð 1Ëèíåéíîå ïðîñòðàíñòâî íàä ïðîèçâîëüíûì ïîëåì1. Îïðåäåëåíèå, ïðèìåðûÀ: 44.5, 9, 4(à,á), 13(àâ), 11(à)Ä: 44.68, 3, 12, 142. Ëèíåéíàÿ çàâèñèìîñòü. Áàçà è ðàíã ñèñòåìû âåêòîðîâ. Èçîìîðôèçì ëèíåéíûõ ïðîñòðàíñòâÀ: 44.19, 20(à), 21(à), 24, 31, 34, 44, 55Ä: 44.2022, 25, 29, 32, 36, 38, 42, 46, 47, 58Ð: 44.23, 39, 56Ñåìèíàð 23.
Áàçèñ, ðàçìåðíîñòü. Êîîðäèíàòû âåêòîðà. Ìàòðèöà ïåðåõîäà ê äðóãîìó áàçèñóÀ: 44.11(á), 62, 6870, 73, 75, 80, 87, 91, 92, 94Ä: 44.11(â), 64, 67, 71(à), 72(à,á), 77, 86, 89, 90, 93Ð: 44.61, 61.1, 91.1Ñåìèíàð 3Ëèíåéíîå ïîäïðîñòðàíñòâî1. Îïðåäåëåíèå, ñïîñîáû çàäàíèÿÀ: 45.2, 3, 6, 12, 13, 17, 24, 27, 33Ä: 45.4, 5, 7, 8, 14, 16(à,ã), 19, 21, 28, 29, 342. Ñóììà ïîäïðîñòðàíñòâÀ: 45.42, 43Ä: 45.40, 41, 44Ð: 45.25, 35, 37, 42.1, 1, 4622Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 4À:Ä:À:Ä:Ð:3.
Ïåðåñå÷åíèå ïîäïðîñòðàíñòâ45.49, 54, 58, 6845.50, 55, 60, 644. Ïðÿìàÿ ñóììà ïîäïðîñòðàíñòâ. Äîïîëíèòåëüíîåïîäïðîñòðàíñòâî45.6971, 73, 74(à), 77, 79, 8245.72, 74(á,â), 76, 7845.63, 66, 67, 80.1, 83Ñåìèíàð 5Ëèíåéíîå àôôèííîå ìíîãîîáðàçèåÀ: 46.3, 7, 14(à,á), 15(à), 16(à), 17, 24, 25, 39, 41, 65Ä: 46.4, 5, 8, 14(â,ä,å), 15(á), 16(á), 19, 21, 26, 27, 37, 42, 64, 68Ð: 46.23, 48, 50, 60Ñåìèíàð 6Åâêëèäîâî (óíèòàðíîå) ïðîñòðàíñòâîÀ:Ä:À:Ä:Ð:1. Ñêàëÿðíîå ïðîèçâåäåíèå. Íåðàâåíñòâî ÊîøèÁóíÿêîâñêîãîØâàðöà.
Äëèíà âåêòîðà47.13, 5(à,á,ä), 6, 10(àâ), 24, 27, 3247.4, 7, 8(àã), 9, 10(ã,ä), 11, 20, 25, 26, 28(à), 332. Îðòîãîíàëüíîñòü âåêòîðîâ48.1, 5, 848.3, 4, 647.32.1, 32.2Ñåìèíàð 73. Îðòîíîðìèðîâàííûé áàçèñ. Ïðîöåññ îðòîãîíàëèçàöèèÀ: 48.10, 11, 14, 17, 19, 21, 24, 25(2,3), 26, 30, 31, 33(1,2), 34(1),37(13)Ä: 48.15(1,2), 20(à), 21.1, 25(1, 46), 28, 32, 33(3,4), 34(2), 37(46)23Àëãåáðà è ãåîìåòðèÿ4. Ìàòðèöà ÃðàìàÀ: 48.38, 41Ä: 47.16.1, 48.39Ð: 47.16.2, 48.47Ñåìèíàð 85. Îðòîãîíàëüíîå äîïîëíåíèå. Çàäà÷à î ïåðïåíäèêóëÿðåÀ: 49.7(á,â), 12(à), 14(à), 15, 17(à,â), 18(à,á), 19, 26(à), 30, 43Ä: 49.7(ã), 9, 12(á,â), 14(á), 16, 17(á,ã), 18(â,ã), 21, 24(à), 26(â), 31,35, 426.
Ìåòðè÷åñêèå çàäà÷èÀ: 50.5(3), 9, 29, 33, 42, 51.17(à,á), 20Ä: 50.5(2), 6, 7, 30, 34, 44, 46, 51.17(â), 18(à), 24Ð: 49.8, 28, 29, 5153, 50.9.1, 9.2, 10, 39.1, 39.2, 45, 45.1, 51.15Ñåìèíàð 9Êîíòðîëüíàÿ ðàáîòà 1 (ñì. ñòð. 36)Òåìû: ëèíåéíîå ïðîñòðàíñòâî, åâêëèäîâî (óíèòàðíîå) ïðîñòðàíñòâîÑåìèíàð 10Ëèíåéíûå îïåðàòîðû â ëèíåéíîì ïðîñòðàíñòâå1. Îïðåäåëåíèå è ïðîñòåéøèå ñâîéñòâàÀ: 52.3, 5(à,á) 6(à,á), 7, 11(à,á), 19Ä: 52.4, 5(â,ä,æ), 6(âä), 810, 12, 202. Ìàòðèöà ëèíåéíîãî îïåðàòîðàÀ: 52.24, 27, 39, 46, 48(á), 54(à), 53.1, 4, 17Ä: 52.25, 28, 40, 42, 48(â), 49(à), 53(à), 53.3, 5, 18Ð: 52.14, 15, 21, 23, 53.21, 22, 26, 3124Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 113. Îáðàç è ÿäðî ëèíåéíîãî îïåðàòîðàÀ: 54.1, 3(à), 5, 9(1), 10(3), 11(1), 14, 17, 21, 27(1), 28(1), 38, 41(1)Ä: 54.2, 3(á), 6, 9(2), 10(2,4), 11(3), 12, 19, 22, 27(2), 28(2), 35,41(2)Ð: 54.25, 26, 39Ñåìèíàð 124.
Ëèíåéíîå ïðîñòðàíñòâî ëèíåéíûõ îïåðàòîðîâÀ: 55.1, 4, 5, 7, 9, 17(à,â), 18(à), 19, 27, 30, 31Ä: 55.2, 3, 6, 8, 10, 17(á,ã), 18(á), 20, 24, 25, 32, 33Ð: 55.23, 3437Ñåìèíàð 135. Óìíîæåíèå îïåðàòîðîâ. Îáðàòíûé îïåðàòîðÀ: 56.1, 4, 79, 13(à,á), 17, 21, 22, 29, 50, 54, 56, 64, 75Ä: 56.2, 3, 6, 12, 19, 20, 23, 30, 52, 65, 76Ð: 56.5, 10, 26, 27, 32, 34, 35, 37, 67, 74Ñåìèíàð 14Ñòðóêòóðà ëèíåéíîãî îïåðàòîðà1. Ñîáñòâåííûå çíà÷åíèÿ è ñîáñòâåííûå âåêòîðû.Õàðàêòåðèñòè÷åñêèé ìíîãî÷ëåíÀ: 57.1, 5, 7, 10, 11, 17, 25(à,â), 34, 41, 50, 51, 73(à,ä), 77Ä: 57.3, 68, 1316, 23, 25(á,å), 30, 32, 35, 37, 43, 59, 73(â,ã,å), 78(à)Ð: 57.63, 64, 74, 8487Ñåìèíàð 152. Îïåðàòîð ïðîñòîé ñòðóêòóðûÀ: 58.1, 2(á), 3, 5, 8, 10, 12, 29, 40, 47(à), 48, 49, 50, 65, 77Ä: 58.2(à,â), 4, 6, 7, 9, 11, 14, 30, 41, 47(á), 51, 52, 66, 67, 73, 75Ð: 58.63, 7825Àëãåáðà è ãåîìåòðèÿÑåìèíàð 163.
Èíâàðèàíòíûå ïîäïðîñòðàíñòâàÀ: 59.2, 4, 11(á,ä), 12(á), 2527, 34, 35(à), 43Ä: 59.3, 5, 6, 11(â,æ), 13, 12(à,â), 17, 28, 32(ã), 35(á), 45, 47Ð: 59.9, 10, 16, 19, 20, 29, 31, 37.1, 37.2Ñåìèíàð 174. Êîðíåâûå ïîäïðîñòðàíñòâàÀ: 60.1, 2(àâ), 3, 5, 7, 11(à), 13, 15, 17Ä: 60.2, 4, 6, 8, 11(á), 14, 16, 20Ð: 60.20.1Ñåìèíàð 185. Æîðäàíîâ áàçèñ è æîðäàíîâà ôîðìà ìàòðèöû ëèíåéíîãî îïåðàòîðàÀ: 60.21, 24, 27, 29, 36, 45, 50, 53Ä: 60.22, 25, 32, 46, 55, 58Ð: 60.37, 38, 59Ñåìèíàð 195. Æîðäàíîâ áàçèñ è æîðäàíîâà ôîðìà ìàòðèöû ëèíåéíîãî îïåðàòîðà (ïðîäîëæåíèå)À: 60.65, 68, 71, 74, 84, 88Ä: 60.70, 72, 73, 75, 86, 89Ð: 60.76, 77, 77.177.8, 80, 83Ñåìèíàð 206.
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