题目内容

已知矩阵\[A = \left[ {\begin{array}{*{20}{c}} 1&2&0&0\\ 2&1&0&0\\ 0&0&3&0\\ 0&0&2&1 \end{array}} \right]\],则`\|A^6|=` ( )

A. \[{3^{12}}\]
B. \[{3^{13}}\]
C. \[{2^{12}}\]
D. \[{2^{13}}\]

查看答案
更多问题

已知`\a=(1,1,1)`,则`\|a^Ta|=` ( )

A. -2
B. -1
C. 0
D. 1

设3阶矩阵`\A = (alpha _1,alpha _2,alpha _3),B = (alpha _2-2alpha _3,alpha _1,alpha _2)`,若`\A`的行列式`\| A | = 2`,则`\ B `的行列式`\| B |= ` ( )

A. -4
B. -2
C. 2
D. 4

设`\A`为`\n`阶方阵,`\A^**`为`\A`的伴随矩阵,且`\| A | = a \ne 0`,则`\| A^**| = ` ( )

A. \[a^{n - 1}\]
B. \[a^n \]
C. \[a^{n + 1}\]
D. \[a^{n + 2}\]

设`\n`阶方阵`\A`经过初等变换后得方阵`\B`,则 ( )

A. \[\left| {\rm{A}} \right| = \left| {\rm{B}} \right|\]
B. \[\left| A \right| \ne \left| B \right|\]
C. \[\left| A \right|\left| B \right| \ge {\rm{0}}\]
D. 若`\| A| = 0`,则`\| B| = 0`

答案查题题库