И.С. Ломов - Алгебра и аналитическая геометрия (1109877), страница 3
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Äåëåíèå îòðåçêàâ äàííîì îòíîøåíèè. Ðàäèóñ-âåêòîð òî÷êèÀ: 13.1, 17, 3, 4, 9, 16, 22, 34, 29.Ä: 13.2, 5, 7, 8, 10, 14, 16.1, 16.2, 23, 33, 35, 37.Ð: 13.42, 45, 46.Ñåìèíàð 9Ëèíåéíîå ïðîñòðàíñòâîÀêñèîìû ëèíåéíîãî ïðîñòðàíñòâà. Ïðèìåðû. Àðèôìåòè÷åñêîå ïðîñòðàíñòâî. Ëèíåéíàÿ çàâèñèìîñòüÀ: 14.1, 5, 7, 8, 15.1, 4, 68, 11, 17, 25, 29.Ä: 14.24, 6, 9, 15.2, 3, 5, 12, 20, 21, 23, 24, 26, 30.Ð: 14.1012, 15.35, 36.14Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 10Ðàíã ìàòðèöû1. Ðàíã ìàòðèöû è ýëåìåíòàðíûå ïðåîáðàçîâàíèÿ å¼ñòðîê è ñòîëáöîâ. Ìåòîä Ãàóññà âû÷èñëåíèÿ ðàíãàÀ: 16.1, 5, 10, 15, 17, 18, 20, 24, 3436.Ä: 16.2, 3, 7, 11, 13, 19, 23, 28.Ð: 16.20.1, 30, 33.Ñåìèíàð 112. Ðàíã ìàòðèöû è ëèíåéíàÿ çàâèñèìîñòü å¼ ñòðîê èñòîëáöîâÀ: 16.38, 39, 42, 55.Ä: 16.37, 40, 41, 43, 60, 61.Ñèñòåìû ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèé1.
Ïðàâèëî ÊðàìåðàÀ: 19.3, 10, 17, 26, 29.Ä: 19.2, 8, 11, 19, 30.Ð: 16.42.1, 44, 44.1, 47, 51, 52, 63, 64, 19.1215, 25.Ñåìèíàð 122. Êðèòåðèé ñîâìåñòíîñòè ñèñòåì îáùåãî âèäàÀ: 20.1, 3, 5, 7, 21.57.Ä: 20.2, 4, 6, 8, 21.55, 59.3. Ìåòîä Ãàóññà èññëåäîâàíèÿ è ðåøåíèÿ ñèñòåì. Îáùåå ðåøåíèåÀ: 21.13, 46(á), 26, 35, 52.Ä: 21.4, 5, 12, 17, 46(à), 47, 53, 27, 33, 48(à), 35.Ð: 20.8, 9, 11, 21.58, 60, 62.Ñåìèíàð 13Ãåîìåòðè÷åñêèå ñâîéñòâà ìíîæåñòâà ðåøåíèé ñèñòåìû1. Ëèíåéíîå ïîäïðîñòðàíñòâî ðåøåíèé îäíîðîäíîéñèñòåìû óðàâíåíèé.
Ôóíäàìåíòàëüíàÿ ñèñòåìà ðåøåíèé. Îáùåå ðåøåíèå15Àëãåáðà è àíàëèòè÷åñêàÿ ãåîìåòðèÿÀ: 22.1, 2, 4, 10, 14, 15.Ä: 22.3, 9, 12, 16.2. Ëèíåéíîå ìíîãîîáðàçèå ðåøåíèé íåîäíîðîäíîéñèñòåìû. Îáùåå ðåøåíèåÀ: 22.20, 26, 30, 33, 35, 3840.Ä: 22.21, 27, 28, 32, 34, 48.Ð: 22.29, 37, 41, 46, 49, 50.Ñåìèíàð 14Êîëëîêâèóì (ñì. ñòð. 29)Ñåìèíàð 15Êîíòðîëüíàÿ ðàáîòà 1 (ñì. ñòð. 31)Òåìû: ìàòðè÷íàÿ àëãåáðà, îïðåäåëèòåëè, ðàíã ìàòðèöû, îáðàòíàÿìàòðèöà, ñèñòåìû ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèé.Ñåìèíàð 16Àôôèííàÿ è ïðÿìîóãîëüíàÿ äåêàðòîâà ñèñòåìû êîîðäèíàò1.
Êîîðäèíàòû òî÷êèÀ: 23.1, 3, 5.Ä: 23.2, 6, 7, 9.2. Äåëåíèå îòðåçêà â äàííîì îòíîøåíèèÀ: 23.19, 14, 26, 33.Ä: 23.20, 17, 22, 29, 34, 35.3. Ïðåîáðàçîâàíèå êîîðäèíàòÀ: 23.39, 43, 48, 62, 63, 56, 67.Ä: 23.38, 47, 49, 51, 53, 57, 64, 66.Ð: 23.55, 65, 65.1.Ñåìèíàð 17Ñêàëÿðíîå ïðîèçâåäåíèåÀ: 24.4, 6, 8, 12, 15, 20, 27, 32, 47, 58, 67, 75, 78.Ä: 24.5, 7, 13, 16, 17, 26, 28, 34, 36, 48, 49, 57, 63, 69, 74, 79.Ð: 24.33, 34.1, 34.2, 3941, 73, 76, 78, 87, 90, 91.16Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 18Âåêòîðíîå è ñìåøàííîå ïðîèçâåäåíèÿÀ: 25.5, 7, 11, 14, 22, 26, 35, 37, 44, 49, 59, 62.Ä: 25.4, 6, 8, 9, 16, 17, 25, 27, 33, 36, 38, 40, 46, 48, 52, 64, 65, 71.Ð: 25.20, 12, 63, 66, 67, 72, 74, 75.Ñåìèíàð 19Ïðÿìàÿ íà ïëîñêîñòèÀ:Ä:À:Ä:À:Ä:Ð:1. Ñïîñîáû çàäàíèÿ26.7, 18, 21.26.8, 10, 15, 19, 20, 22, 24.2.
Âçàèìíîå ðàñïîëîæåíèå ïðÿìûõ27.8, 15, 20, 25.27.10, 13, 16, 22, 24.3. Ïîëóïëîñêîñòè28.4, 11, 20.28.6, 9, 13.26.27, 27.26, 28.Ñåìèíàð 204. Ìåòðè÷åñêèå çàäà÷èÀ: 29.1, 6, 18, 33, 37, 44(1), 45(1), 56.Ä: 29.35, 9, 35, 38, 43, 44(2), 45(2), 55, 57, 78.Ïëîñêîñòü â ïðîñòðàíñòâå1. Ñïîñîáû çàäàíèÿÀ: 26.31, 39, 44.Ä: 26.29, 32, 34, 38, 50.Ð: 29.39, 65.17Àëãåáðà è àíàëèòè÷åñêàÿ ãåîìåòðèÿÑåìèíàð 21À:Ä:À:Ä:À:Ä:Ð:2. Âçàèìíîå ðàñïîëîæåíèå ïëîñêîñòåé27.37, 40.27.35, 33, 39, 49.3. Ïîëóïðîñòðàíñòâà28.20.28.17, 18.4.
Ìåòðè÷åñêèå çàäà÷è29.79, 88.29.81, 83, 89, 93, 102.27.53, 54, 28.19, 21, 23, 29.91, 92.Ñåìèíàð 22Ïðÿìàÿ â ïðîñòðàíñòâåÀ:Ä:À:Ä:Ð:1. Ñïîñîáû çàäàíèÿ. Ðàñïîëîæåíèå ïðÿìûõ â ïðîñòðàíñòâå31.2(1),4(1), 11(2), 13, 18(1,2), 23.31.1, 2(2), 3, 4(2), 5, 11(1), 14, 15, 18(3,4), 19, 24, 31, 34.2. Ìåòðè÷åñêèå çàäà÷è32.3, 5, 8, 13, 20, 34, 39.32.10, 17, 21, 26, 36, 37, 38.32.32.1, 31.36, 32.40, 42.Ñåìèíàð 23Âåêòîðíûå óðàâíåíèÿ ïðÿìîé è ïëîñêîñòèÀ: 33.5, 8, 10, 15, 20, 26, 29, 35, 41.Ä: 33.6, 7, 11, 12, 22, 23, 27, 30, 36, 40.Ð: 33.1, 31, 33, 41, 42, 44.Ñåìèíàð 24Êîíòðîëüíàÿ ðàáîòà 2 (ñì.
ñòð. 32)Òåìû: äåëåíèå îòðåçêà â îòíîøåíèè, ïðåîáðàçîâàíèå êîîðäèíàò,ñêàëÿðíîå, âåêòîðíîå è ñìåøàííîå ïðîèçâåäåíèÿ, ïðÿìàÿ íàïëîñêîñòè, ïëîñêîñòü â ïðîñòðàíñòâå, ïðÿìàÿ â ïðîñòðàíñòâå.18Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 25Ýëåìåíòû îáùåé àëãåáðûÀ:Ä:À:Ä:Ð:1. Ãðóïïà. Ïðèìåðû ãðóïï. Ïðîñòåéøèå ñâîéñòâà39.1(18), 2(18), 3(15), 4(1,2), 8, 10.39.1(917), 2(918), 3(613), 4(35), 5, 9.2. Èçîìîðôèçì ãðóïï39.11, 13, 14, 17, 20.39.12, 16, 19, 21, 24.39.23.Ñåìèíàð 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, 64.39.53(â,ä), 54(á), 59, 60, 65, 72.39.83, 55.Ñåìèíàð 275. Êîëüöî è ïîëåÀ: 40.14, 8, 10, 11, 26, 27, 33, 38.Ä: 40.14, 8, 12, 13, 15, 30, 32, 39.Ð: 40.40, 47, 48, 54, 56, 58.Ñåìèíàð 28Êîìïëåêñíûå ÷èñëà1. Ïîëå êîìïëåêñíûõ ÷èñåëÀ: 41.1(à,ã,å), 5(à), 6(à), 7, 9(à), 10(â,ã), 11(à), 15.Ä: 41.1, 5, 6(á), 8, 9(á), 10(á,ä,å), 11, 16, 21.Ð: 41.13, 23.19Àëãåáðà è àíàëèòè÷åñêàÿ ãåîìåòðèÿÑåìèíàð 29À:Ä:À:Ä:Ð:2.
Òðèãîíîìåòðè÷åñêàÿ ôîðìà çàïèñè êîìïëåêñíîãî÷èñëà. Ôîðìóëà Ìóàâðà42.13, 8, 23(à), 27, 32.42.1, 3, 5, 6, 9, 10, 23(á), 28, 31(à,á).3. Èçâëå÷åíèå êîðíÿ43.2, 6, 7, 11, 15(à,â), 20, 25.43.13, 5, 8, 9, 1417, 21, 23, 24, 27.42.19, 21, 21.1, 43.29, 32, 32.1.Ñåìèíàð 30Ëèíèè âòîðîãî ïîðÿäêà íà ïëîñêîñòè1. Ýëëèïñ, ãèïåðáîëà, ïàðàáîëàÀ: 34.1, 6, 13, 18, 20, 26, 32, 36, 40, 49, 61, 66.Ä: 34.1, 4, 9, 11, 13, 16, 2224, 29, 39, 44, 58, 64, 65.Ð: 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, 27.Ð: 35.7, 9.1, 17, 26, 28.Ñåìèíàð 32Ïîâåðõíîñòè âòîðîãî ïîðÿäêà1. Ýëëèïñîèä, ãèïåðáîëîèäû, ïàðàáîëîèäûÀ: 36.1, 5, 8(1), 13(1), 17, 18, 33, 40, 46.Ä: 36.3, 6, 8(2), 13(2,3), 19, 20, 23, 32, 36, 47, 52.2. Êîíóñû, öèëèíäðûÀ: 37.1, 6, 8, 16.Ä: 37.2, 5, 7, 15, 19.3. Ïîâåðõíîñòè, çàäàííûå îáùèì óðàâíåíèåìÀ: 38.1, 9(1,2), 10, 11(1,2), 12(2).Ä: 38.4, 6(1), 712.Ð: 36.1114, 25, 31, 33.1, 4344.1, 51, 53, 37.18, 21, 22, 38.2.20Ñåìèíàðñêèå çàíÿòèÿÏëàí ñåìèíàðñêèõ çàíÿòèé, II ñåìåñòðÑåìèíàð 1Ëèíåéíîå ïðîñòðàíñòâî íàä ïðîèçâîëüíîì ïîëåì1. Îïðåäåëåíèå, ïðèìåðûÀ: 44.5, 9, 4(à,á), 13(àâ), 11(à).Ä: 44.68, 3, 12, 14.2.
Ëèíåéíàÿ çàâèñèìîñòü. Áàçà è ðàíã ñèñòåìû âåêòîðîâ. Èçîìîðôèçì ëèíåéíûõ ïðîñòðàíñòâÀ: 44.19, 20(à), 21(à), 24, 31, 34, 44, 55.Ä: 44.2022, 25, 29, 32, 36, 38, 42, 46, 47, 58.Ð: 44.23, 39, 56.Ñåìèíàð 23. Áàçèñ, ðàçìåðíîñòü. Êîîðäèíàòû âåêòîðà. Ìàòðèöà ïåðåõîäà ê äðóãîìó áàçèñóÀ: 44.11(á), 62, 6870, 73, 75, 80, 87, 91, 92, 94.Ä: 44.11(â), 64, 67, 71(à), 72(à,á), 77, 86, 89, 90, 93.Ð: 44.61, 61.1, 91.1.Ñåìèíàð 3Ëèíåéíîå ïîäïðîñòðàíñòâî1. Îïðåäåëåíèå, ñïîñîáû çàäàíèÿÀ: 45.2, 3, 6, 12, 13, 17, 24, 27, 33.Ä: 45.4, 5, 7, 8, 14, 16(à,ã), 19, 21, 28, 29, 34.2. Ñóììà ïîäïðîñòðàíñòâÀ: 45.42, 43.Ä: 45.40, 41, 44.Ð: 45.25, 35, 37, 42.1, 1, 46.21Àëãåáðà è àíàëèòè÷åñêàÿ ãåîìåòðèÿÑåìèíàð 4À:Ä:À:Ä:Ð:3.
Ïåðåñå÷åíèå ïîäïðîñòðàíñòâ45.49, 54, 58, 68.45.50, 55, 60, 64.4. Ïðÿìàÿ ñóììà ïîäïðîñòðàíñòâ. Äîïîëíèòåëüíîåïîäïðîñòðàíñòâî45.6971, 73, 74(à), 77, 79, 82.45.72, 74(á,â), 76, 78.45.63, 66, 67, 80.1, 83.Ñåìèíàð 5Ëèíåéíîå àôôèííîå ìíîãîîáðàçèåÀ: 46.3, 7, 14(à,á), 15(à), 16(à), 17, 24, 25, 39, 41, 65.Ä: 46.4, 5, 8, 14(â,ä,å), 15(á), 16(á), 19, 21, 26, 27, 37, 42, 64, 68.Ð: 46.23, 48, 50, 60.Ñåìèíàð 6Åâêëèäîâî (óíèòàðíîå) ïðîñòðàíñòâîÀ:Ä:À:Ä:Ð:1. Ñêàëÿðíîå ïðîèçâåäåíèå.
Íåðàâåíñòâî ÊîøèÁóíÿêîâñêîãîØâàðöà. Äëèíà âåêòîðà47.13, 5(à,á,ä), 6, 10(àâ), 24, 27, 32.47.4, 7, 8(àã), 9, 10(ã,ä), 11, 20, 25, 26, 28(à), 33.2. Îðòîãîíàëüíîñòü âåêòîðîâ48.1, 5, 8.48.3, 4, 6.47.32.1, 32.2.Ñåìèíàð 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, 25, 28, 32, 33(3,4), 34(2), 37(46).22Ñåìèíàðñêèå çàíÿòèÿ4. Ìàòðèöà ÃðàìàÀ: 48.38, 41.Ä: 47.16.1, 48.39.Ð: 47.16.2, 48.47.Ñåìèíàð 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, 43.Ä: 49.7(ã), 9, 12(á,â), 14(á), 16, 17(á,ã), 18(â,ã), 21, 24(à), 26(â), 31,35, 42.6. Ìåòðè÷åñêèå çàäà÷èÀ: 50.5(3), 9, 29, 33, 42, 51.17(à,á), 20.Ä: 50.5(2), 6, 7, 30, 34, 44, 46, 51.17(â), 18(à), 24.Ð: 49.8, 28, 29, 5153, 50.9.1, 9.2, 10, 39.1, 39.2, 45, 45.1, 51.15.Ñåìèíàð 9Êîíòðîëüíàÿ ðàáîòà 1 (ñì. ñòð. 33)Òåìû: ëèíåéíîå ïðîñòðàíñòâî, åâêëèäîâî (óíèòàðíîå) ïðîñòðàíñòâî.Ñåìèíàð 10Ëèíåéíûå îïåðàòîðû â ëèíåéíîì ïðîñòðàíñòâå1.
Îïðåäåëåíèå è ïðîñòåéøèå ñâîéñòâàÀ: 52.3, 5(à,á) 6(à,á), 7, 11(à,á), 19.Ä: 52.4, 5(â,ä,æ), 6(âä), 810, 12, 20.2. Ìàòðèöà ëèíåéíîãî îïåðàòîðàÀ: 52.24, 27, 39, 46, 48(á), 54(à), 53.1, 4, 17.Ä: 52.25, 28, 40, 42, 48(â), 49(à), 53(à), 53.3, 5, 18.Ð: 52.14, 15, 21, 23, 53.21, 22, 26, 31.23Àëãåáðà è àíàëèòè÷åñêàÿ ãåîìåòðèÿÑåìèíàð 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, 39.Ñåìèíàð 124. Ëèíåéíîå ïðîñòðàíñòâî ëèíåéíûõ îïåðàòîðîâÀ: 55.1, 4, 5, 7, 9, 17(à,â), 18(à), 19, 27, 30, 31.Ä: 55.2, 3, 6, 8, 10, 17(á,ã), 18(á), 20, 24, 25, 32, 33.Ð: 55.23, 3437.Ñåìèíàð 135. Óìíîæåíèå îïåðàòîðîâ.
Îáðàòíûé îïåðàòîðÀ: 56.1, 4, 79, 13(à,á), 17, 21, 22, 29, 50, 54, 56, 64, 75.Ä: 56.2, 3, 6, 12, 19, 20, 23, 30, 52, 65, 76.Ð: 56.5, 10, 26, 27, 32, 34, 35, 37, 67, 74.Ñåìèíàð 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), 77.Ä: 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, 8487.Ñåìèíàð 152.
Îïåðàòîð ïðîñòîé ñòðóêòóðûÀ: 58.1, 2(á), 3, 5, 8, 10, 12, 29, 40, 47(à), 48, 49, 50, 65, 77.Ä: 58.2(à,â), 4, 6, 7, 9, 11, 14, 30, 41, 47(á), 51, 52, 66, 67, 73, 75.Ð: 58.63, 78.24Ñåìèíàðñêèå çàíÿòèÿÑåìèíàð 163. Èíâàðèàíòíûå ïîäïðîñòðàíñòâàÀ: 59.2, 4, 11(á,ä), 12(á), 2527, 34, 57.35(à), 43.Ä: 59.3, 5, 6, 11(â,æ), 13, 12(à,â), 17, 28, 32(ã), 35(á), 45, 47.Ð: 59.9, 10, 16, 19, 20, 29, 31, 37.1, 37.2.Ñåìèíàð 174. Êîðíåâûå ïîäïðîñòðàíñòâàÀ: 60.1, 2(àâ), 3, 5, 7, 11(à), 13, 15, 17.Ä: 60.2, 4, 6, 8, 11(á), 14, 16, 20.Ð: 60.20.1.Ñåìèíàð 185. Æîðäàíîâ áàçèñ è æîðäàíîâà ôîðìà ìàòðèöû ëèíåéíîãî îïåðàòîðàÀ: 60.21, 24, 27, 29, 36, 45, 50, 53.Ä: 60.22, 25, 32, 46, 55, 58.Ð: 60.37, 38, 59.Ñåìèíàð 195. Æîðäàíîâ áàçèñ è æîðäàíîâà ôîðìà ìàòðèöû ëèíåéíîãî îïåðàòîðà (ïðîäîëæåíèå)À: 60.65, 68, 71, 74, 84, 88.Ä: 60.70, 72, 73, 75, 86, 89.Ð: 60.76, 77, 77.177.8, 80, 83.Ñåìèíàð 206.
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