题目内容

`\A`为3阶方阵,且`\|A|=2`,则`\| ( 2A)^{ - 1} + 2A^**| = ` ( )

A. \[\frac{{729}}{{16}}\]
B. \[\frac{{729}}{{32}}\]
C. \[\frac{{263}}{{16}}\]
D. \[\frac{{263}}{{32}}\]

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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. \[{2^{13}}\]

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. \[a^{n + 2}\]

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