?5?2 (1)?0?0?210000850?0?? 3?2??5 解 设A???2?5 A?1???2?2?? B??8?51????13?? 则 2??3???2?3??
??58?2?????12???1?2?? B?1??8??25??51??????1?5?2于是 ?0?0??1?1 (2)?2?1?02122100003100850??1?200??1?10???A???A????2500??
???1??03??02?3B?B???????2?00?58??0?0?? 0?4??1 解 设A???1?
0?? B??30?? C??21?? 则
?14??12?2???????1?1?1 ?2?1?021200310??10???AO???A?1O?
????1?1?0CB???BCAB?1????4?0??0??? 0?1??4?00?1?11?0?22?1 ??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?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???10003111?4?2?2?23?2?(下一步? r?3r? r?r? r?r? )
123242
2?2???1?0 ~?0?0??100002?3?1?22?? 000?000???23?12 (4)?3?2?2?3?1?3?7?0?2?4?? 830?743??1?3?7?0?2?4?(下一步? r?2r? r?3r? r?2r? )
123242
830?743???23?12 解 ?3?2?2?3??0?1111?