工程数学线性代数课后习题答案

?5200??1?200??1?1于是 ??21?3????A???A?1?0?????200080?052???B???B?1????0?0??10 (2)?120?21000??

?12310?4?? 解 设A???10?12??? B???304??1? C???2?11?2???

?100?1 ??1200???1?2100????AO??12314???CB?????A?1??B?1CA?1BO?1?????1000???110?? ??220??110??

?2?163?11??8?524?1124??

5002?0?3?

0?58??则

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

?304?3??? r2(

2)r1 r3(3)r1 )

?102?1? ~?00?13?(下一步

?00?20????102?1? ~?001?3?(下一步

?0010??? r2(1) r3(2)

)

r3r2 )

~???010021??31??(下一步

r33

)

?0003?? ~??1?00021??13??(下一步

r23r3 )

?0001?? ~??102?1?0010??(下一步

r1(

2)r2 r1r3 )

?0001?? ~??1?0000100??

?0001?? (2)??0?023??341?

?04?7?3?1?? 解 ??02?31??03?43?(下一步

r22(3)r1 r3(?04?7?1?? ~??0?020?3131??(下一步

r3r2 r13r2 )

?00?1?3?? ~??020?001103??(下一步

r12

)

?0000?? ~??01?000153??

?0000????13 (3)?3???315??43?2?41???3?2334?220?

?1??2)r1

)

?1?3 解 ?2?3??1?3?2?33534?4?4?2?23?1?(下一步0??1?? r23r1 r32r1 r43r1 )

?1?13?43??00?48?8? ~?(下

00?36?6??00?510?10???r(5) )

?1?13?43??001?22? ~?(下一步 r001?22??001?22???4

一步 r2(4) r3(3)

1

3r2 r3r2 r4r2 )

?1?0 ~?0?0??100002?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

3?2830??2?3743????0?1 ~?0?0??0?1 ~?0?0??12?8?7?1000111?0?2?4?(下一步8912?7811??120011?0?2?(下一步14?14?? r12r2 r33r2 r42r2 )

r22r1 r38r1 r47r1 )

r1r2 r2(1) r4

r3 )