设 \( A \)是 \( 3 \times 3 \)矩阵, \( B \)是 \( 4 \times 4 \)矩阵,且\( \left| A \right| = 1,\,\left| B \right| = - 2, \) 则\( \left| {\left| B \right|A} \right| = \) ______
-8
举一反三
- 设\( \left| { { x_0}} \right| = 4 \),\( A \)为正交矩阵,则\( \left| {A{x_0}} \right| = \)______
- 设`\A`是`\m \times n`矩阵,`\m` 小于 `\n`,则必有 ( ) A: \[\left| {{A^T}A} \right| \ne 0\] B: \[\left| {{A^T}A} \right| = 0\] C: \[\left| {A{A^T}} \right| > 0\] D: \[\left| {A{A^T}} \right| < 0\]
- 函数\(y = {\left( { - 2x + 1} \right)^4}\)的导数为( ). A: \( - 8{\left( { - 2x + 1} \right)^3}\) B: \(8{\left( { - 2x + 1} \right)^3}\) C: \(4{\left( { - 2x + 1} \right)^3}\) D: \(- 4{\left( { - 2x + 1} \right)^3}\)
- 设 \( A \)为 \( m \times n \)矩阵, \( B \)为 \( n \times m \)矩阵,则下列结论中不正确的是( ) A: \( {\left( {AB} \right)^T} = {B^T}{A^T} \) B: \( \left| {AB} \right| = \left| {BA} \right| \) C: \( tr\left( {AB} \right) = tr\left( {BA} \right) \) D: \( {A^T}A,\;B{B^T} \)均为\(n\)阶对称阵
- 设\( {\bf{A}} \) 为三阶矩阵,\( { { \bf{A}}^*} \)是\( {\bf{A}} \)的伴随矩阵,且\( \left| {\bf{A}} \right| = 1 \),则\( \left| {2 { { \bf{A}}^{ - 1}} + 3 { { \bf{A}}^*}} \right| = \)______
内容
- 0
设\( A \) 是\( 3 \) 阶矩阵,且\( \left| A \right| = 3 \) ,则 \( \left| { - 3A} \right| = \)( ) A: -9 B: 9 C: -81 D: 81
- 1
设\( {\alpha _1} = {\left( {1,2, - a, - 3} \right)^T},{\alpha _2} = {\left( { - 3,2,4,1} \right)^T} \)且\( \left( { { \alpha _1},{\alpha _2}} \right) = - 1 \),则\( a = \)( ) A: \( - {2 \over 3} \) B: \( - {3 \over 4} \) C: \( - {1 \over 4} \) D: \( {1 \over 2} \)
- 2
设\( A \)是3阶矩阵,若\( \left| {3A} \right| = 3 \),则\( \left| {2A} \right| = \)( ) A: 1 B: 2 C: \( {2 \over 3} \) D: \( {8 \over 9} \)
- 3
(4). 设每年袭击某地的台风次数 \( X\sim P\left( \lambda \right) \),且\( P\left\{ {X=1} \right\}=P\left\{ {X=2} \right\} \),则概率 \(P\left\{ {X=4} \right\} =\)()。
- 4
若\( A \)是正交矩阵,则\( \left| A \right| = 1 \)或\( \left| A \right| = - 1 \) .