设\[D = \left| {\begin{array}{*{20}{c}} a&b&c&d\\ c&b&d&a\\ d&b&c&a\\ a&b&d&c \end{array}} \right| = \Delta ({a_{{\rm{ij}}}})\],`\A_{ij}`表示元素`\a_{ij}`的代数余子式,则`\A_{14} + A_{24} + A_{34} + A_{44} = `( )
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\[A = \left[ {\begin{array}{*{20}{c}} 2&2&3\\ 2&3&1\\ 3&4&4 \end{array}} \right]\],且`\BA = A + B`,则矩阵`\B=` ( )
A. \[\left[ {\begin{array}{*{20}{c}}2&3&{ - 2}\\{\frac{3}{2}}&{ - 2}&{ - \frac{5}{2}}\\1&1&0\end{array}} \right]\]
B. \[\left[ {\begin{array}{*{20}{c}}2&3&{ - 2}\\{ - \frac{3}{2}}&{ - 2}&{\frac{5}{2}}\\1&0&0\end{array}} \right]\]
C. \[\left[ {\begin{array}{*{20}{c}}3&3&{ - 2}\\{ - \frac{3}{2}}&2&{\frac{5}{2}}\\1&0&0\end{array}} \right]\]
D. \[\left[ {\begin{array}{*{20}{c}}2&3&{ - 2}\\{ - \frac{3}{2}}&{ - 2}&{\frac{5}{2}}\\1&1&0\end{array}} \right]\]
`\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. \[\frac{{263}}{{32}}\]
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