工程数学线性代数课后习题答案 - 图文

?1111? ? ?1?1 ?r1????r2?1??1?11r?1?1 ?2 ?? ? r3?n? ??1 ?1? ?1 ?111?? ? ?n??2n? ??1 ??1? ?? ??3n? ?? ?4?? ?? ??? 10? ??0? ?c?1?2???c?1??11?200? 0c?200? ?? ??0? ?? ?0 ?3 ? ?? c1?n? ??1 ?12n? ?2? ???232n? ?2?02? ?42n? ?? ?5?? ? ? ? ??n? 0?? ?1(1)

n1

(n1)2n2

1?a11? ? ?1Da? ? ?1n?11?? 1? ?? 21? ??? ?? ??1?? ? , 其中a1a2 a?n解

1?a11? ? ?1 Dn?11?a? ? ?1? 21? ?? 1? ??? ?? ??1?? ? a?na100? ? ?001c1?ca0? ? ?001 ????2?a02?a2a? ? ?001c?? ? ? ?2 ? ?? c3? 0? ?0? ?30?3 ?? ?? ???? a? ?a? ? ?? ? ?000? ? ?0n?1?na?11n1?ann0

(6) a 1?1 ?a1a2? ? ?an0? ? ?0001?1? ? ?00001? ? ?00? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?000? ? ??100a1?1?10a2?10a3

? ? ?? ? ??11an?1?1?11?an100 ?a1a2? ? ?an? ? ?0010? ? ?0001? ? ?0? ? ?? ? ?? ? ?? ? ?? ? ?000? ? ?0000? ? ?1a1?1?1a2?1a3? ? ??1an?1ni?1

000? ? ?001??ai?1 ?(a1a2?an)(1??1)i?1ai

8 用克莱姆法则解下列方程组

n

?x1?x2?x3?x4?5? (1)?x1?2x2?x3?4x4??22x1?3x2?x3?5x4??2?3x?x?2x?11x?0?1234 解 因为

1 D?12312?311?1?1214??142?511

52 D1???2012?311?1?1214??142?5111 D2?1235?2?201?1?1214??284?511

1 D3?1212?35?2?214??426?51 D4?1212?31?1?15?2?142?2

31011所以 xDD1?1D?1 x2?2D?2?5?1 (2)?x1?56xx2?x?1?x2?6x3?0?2?5x?x?3?x5?x6x?46x?034?51?04?5x5

解 因为 5600 D?10560001600050105016?665 5160 D056001?0015001001600516?15075561 D?1000305010000000601516?7035560 D15605?00150160000105010?2121所以

3120 xDD3?3?4D3 x4?D??1

510D?1060000200000560110516??1145

556D1504?0016100005000100016??395

5

x1?1507665 x2??1145665

x3?703665取何值时

x4??395665 x4?212665

9 问 齐次线性方程组

???x1?x2?x3?0?x1??x2?x3?0有非零解？ ??x1?2?x2?x3?0 解 系数行列式为

?11 D?1?1?????12?1 令D0 于是 10

问 当

得 0或0或

1

1时该齐次线性方程组有非零解取何值时

齐次线性方程组

??(1??)x1?2x2?4x3?0?2x1?(3??)x2?x3?0有非零解？ ??x1?x2?(1??)x3?0 解 系数行列式为

1???241???3??4 D?23??1?21??1

111??101?? (1

)

3

((1 得 0

3))

3

4(12(12或

)2(1)3

2

)(33

)

令D0