• 2022-06-14
    若\( A \)是正交矩阵,则\( \left| A \right| = 1 \)或\( \left| A \right| = - 1 \) .
  • 正确

    内容

    • 0

      若\( A,B,\left( {A + B} \right) \)为同阶可逆方阵,则\( {\left( { { B^{ - 1}} + {A^{ - 1}}} \right)^{ - 1}} = \)( ) A: \( {B^{ - 1}} + {A^{ - 1}} \) B: \( B + A \) C: \( {\left( {B + A} \right)^{ - 1}} \) D: \( B{\left( {B + A} \right)^{ - 1}}A \)

    • 1

      设\( A,B \)均为\( n \)阶方阵,则必有( ) A: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) B: \( AB = BA \) C: \( \left| {AB} \right| = \left| {BA} \right| \) D: \( {\left( {A + B} \right)^{ - 1}} = {A^{ - 1}} + {B^{ - 1}} \)

    • 2

      函数$y = \ln x$,则${\left( {\ln x} \right)^{\left( n \right)}} = {\left( { - 1} \right)^{n - 1}}{{\left( {n - 1} \right)!} \over {{x^n}}}$。( )

    • 3

      设\( A \)为\( n \) 阶方阵, \( B \)是\( A \)经过若干次初等变换后得到的矩阵,则( ) A: \( \left| A \right| = \left| B \right| \) B: \( \left| A \right| \ne \left| B \right| \) C: 若\( \left| A \right| = 0 \) ,则必有 \( \left| B \right| = 0 \) D: 若\( \left| A \right| > 0 \),则一定有\( \left| B \right| > 0 \)

    • 4

      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\( \left| {2 { { \bf{A}}^{ - 1}} + 3 { { \bf{A}}^*}} \right| = \)______