AO??D1D2?? 则 解 设??CB???DD????34??1D1D2??AD1AD2??EnO?AO??? ???DD???CD?BDCD?BD???OE?? CB???34??1324??s??D1?A?1?AD1?En?D?O?由此得 ?AD2?O??2?

CD1?BD3?OD3??B?1CA?1?D?B?1?CD?BD?E?24s?4?1AOA??? ?????1?1O所以 ???1?CB?BCAB?????1 30? 求下列矩阵的逆阵?

?5?2 (1)?0?0?210000850?0?? 3?2??2?? B??8?51????15 解 设A???2?5 A?1???2?3?? 则 2??3???2?3??

??58?2?????12???1?2?? B?1??8??25??51??????1?5?2于是 ?0?0?210000850??1?200??1?10???A???A????2500??

????1??03??02?3BB???????2?00?58???1?1 (2)?2?1?021200310?0?? 0?4??1 解 设A???1?0?? B??3?12???0?? C??2?14???1?? 则 2??

?1?1 ?2?1?021200310??1?0??AO???A?1O?

????1?10??CB???BCAB?1???4?0??0??? 0?1??4??100?1?11?0?221 ???1?1?263?15??1??82412

第三章 矩阵的初等变换与线性方程组

1? 把下列矩阵化为行最简形矩阵?

?102?1? (1)?2031??

?304?3????102?1? 解 ?2031?(下一步? r2?(?2)r1? r3?(?3)r1? )

?304?3????102?1? ~?00?13?(下一步? r2?(?1)? r3?(?2)? )

?00?20????102?1? ~?001?3?(下一步? r3?r2? )

?0010????102?1? ~?001?3?(下一步? r3?3? )

?0003????102?1? ~?001?3?(下一步? r2?3r3? )

?0001????102?1? ~?0010?(下一步? r1?(?2)r2? r1?r3? )

?0001????1000? ~?0010??

?0001????02?31? (2)?03?43??

?04?7?1????02?31? 解 ?03?43?(下一步? r2?2?(?3)r1? r3?(?2)r1? )

?04?7?1????02?31? ~?0013?(下一步? r3?r2? r1?3r2? )

?00?1?3????02010? ~?0013?(下一步? r1?2? )

?0000????0105? ~?0013??

?0000????1?13?43??3?35?41? (3)??

2?23?20??3?34?2?1????1?3 解 ?2?3??1?0 ~?0?0??1?3?2?33534?4?4?2?23?1?(下一步? r?3r? r?2r? r?3r? )

213141

0??1???13?43?0?48?8?(下一步? r?(?4)? r?(?3) ? r?(?5)? )

234

0?36?6?0?510?10???1?0 ~?0?0??1?0 ~?0?0??1000?10003111?4?2?2?23?2?(下一步? r?3r? r?r? r?r? )

123242

2?2??02?3?1?22?? 000?000???231?3?7??120?2?4? (4)??

3?2830??2?3743????231?3?7??120?2?4? 解 ?(下一步? r1?2r2? r3?3r2? r4?2r2? )

3?2830??2?3743????0?1 ~?0?0??0?1 ~?0?0??1?0 ~?0?0??1?0 ~?0?0??12?8?7?100001000100111?0?2?4?(下一步? r?2r? r?8r? r?7r? )

213141

8912?7811??120011?0?2?(下一步? r?r? r?(?1)? r?r? )

12243

14?14??0?1100010?2??1?(下一步? r?r? )

23

4?0??2?1002?100?2?3?? 4?0??