A: \({2^{n + 1}} \)
B: \({2^{n }}\)
C: \({2^{n - 1}}\)
D: \(2\)
举一反三
- 设\( A,\;B \) 均为\( n \) 阶方阵,则必有( ). A: \( {(A + B)^2} = {A^2} + 2AB + {B^2} \) B: \( \left| {A + B} \right| = \left| A \right| + \left| B \right| \) C: \( \left| {AB} \right| = \left| A \right|{\kern 1pt} \left| B \right| \) D: \( {\left( {AB} \right)^{\rm T}} = {A^{\rm T}}{B^{\rm T}} \)
- 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\( \alpha {\rm{ = }}\left( {\matrix{ 1 \cr 0 \cr 1 \cr } } \right)\;A = \alpha {\alpha ^{T,}} \) ,则\( \left| {I - {A^n}} \right| = \) ( ) A: \( 1 + {2^n} \) B: \( 1 - {2^n} \) C: \( 1 + {3^n} \) D: \( 1 - {3^n} \)
- 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: \( {a^n} \)
- 设\( A \) 为 \( n \)阶方阵,则 \( \left| {5A} \right| = 5\left| A \right| \).
内容
- 0
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: \( {\left( {A + B} \right)^{ - 1}} = {A^{ - 1}} + {B^{ - 1}} \)
- 1
\( {1 \over {1 + x}} \)的麦克劳林公式为( )。 A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \) D: \( {1 \over {1 + x}} = 1 - x - { { {x^2}} \over 2}- \cdots - { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)
- 2
设\( n \) 阶方阵 \( A,B \)相似,则 \( \left| A \right| = \left| B \right| \).
- 3
函数$y = \ln x$,则${\left( {\ln x} \right)^{\left( n \right)}} = {\left( { - 1} \right)^{n - 1}}{{\left( {n - 1} \right)!} \over {{x^n}}}$。( )
- 4
\( {1 \over {1 + x}} \)的麦克劳林公式为( ). A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \)