设 \( A \)为 \( n \)阶方阵,且\( \left| A \right| = a \ne 0 \) ,则 \( \left| { { A^ * }} \right| = \)( )
A: \( a \)
B: \( {1 \over a} \)
C: \( {a^{n - 1}} \)
D: \( {a^n} \)
A: \( a \)
B: \( {1 \over a} \)
C: \( {a^{n - 1}} \)
D: \( {a^n} \)
举一反三
- 设\( A \) 为 \( n \)阶方阵且 \( \left| A \right| \ne 0 \),则 \( {(2A)^{ - 1}} = \)( ) A: \( {1 \over 2}{A^{ - 1}} \) B: \( {2^{n - 1}}{A^{ - 1}} \) C: \( {2^n}{A^{ - 1}} \) D: \( 2{A^{ - 1}} \)
- 设\(A\)为\(n\)阶方阵,\(\left| A \right| = 2 \),则\(\left| {\left| A \right|{A^T}} \right|=\) A: \({2^{n + 1}} \) B: \({2^{n }}\) C: \({2^{n - 1}}\) D: \(2\)
- 设 \( A \), \( B \)为 \( n \)阶方阵,已知\( A \ne B \) ,则 \( \left| A \right| \ne \left| B \right| \).
- 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`
- 函数$y = \ln x$,则${\left( {\ln x} \right)^{\left( n \right)}} = {\left( { - 1} \right)^{n - 1}}{{\left( {n - 1} \right)!} \over {{x^n}}}$。( )