《线性代数与概率统计》作业题(题目)

《线性代数与概率统计》

作业题

第一部分 单项选择题 1.计算

x1?1x1?2x?1x??( )

22?2A.x1?x2 B.x1?x2 C.x2?x1 D.2x2?x1

1112.行列式D??111??

?1?11A.3 B.4 C.5 D.6

?23?1?3.设矩阵A???111??123?,B??112?,求AB=???11???1??0???01??A.-1

B.0 C.1 D.2

??x1?x2?x3?04.齐次线性方程组??x1??x2?x3?0有非零解,则?=?( ??x1?x2?x3?0A.-1

1

) B.0 C.1 D.2

?00?5.设A???19766??????0905???3?,B???53?,求AB=?( ) ??76???A.??104110??6084??

B.??104111??6280??

C.??104111??6084??

D.??104111??6284??

6.设A为m阶方阵,B为n阶方阵,且A?a,B?b,C???0?BA.(?1)mab B.(?1)nab C.(?1)n?mab

D.(?1)nmab

?123?7.设A???221??,求A?1=?( ) ??343??2

A?0??,则C=?( ) ??132?A.?3?35???2??2? ?11?1????13?2?? B.?35??? ?232??11?1????13?2?? C.?3??352?? ?2?11?1????13?2?D.?3???35??22?? ?11?1??

8.设A,B均为n阶可逆矩阵,则下列结论中不正确的是( )

A.[(AB)T]?1?(A?1)T(B?1)T B.(A?B)?1?A?1?B?1

C.(Ak)?1?(A?1)k(k为正整数)

D.(kA)?1?k?nA?1(k?0) (k为正整数)

9.设矩阵Am?n的秩为r,则下述结论正确的是( ) A.A中有一个r+1阶子式不等于零

B.A中任意一个r阶子式不等于零 C.A中任意一个r-1阶子式不等于零 D.A中有一个r阶子式不等于零

??1?3?10.初等变换下求下列矩阵的秩,A??32?2?131???705?1?的秩为?(??3

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