设向量组\( {\left( {2,1,1,1} \right)^T},{\left( {2,1,a,a} \right)^T},{\left( {3,2,1,a} \right)^T},{\left( {4,3,2,1} \right)^T} \) 线性相关，且\( a \ne 1 \) ，则 \( a = \)______
举一反三
- 设\( {\alpha _1} = {\left( {1,2, - a, - 3} \right)^T},{\alpha _2} = {\left( { - 3,2,4,1} \right)^T} \)且\( \left( { { \alpha _1},{\alpha _2}} \right) = - 1 \)，则\( a = \)（ ） A: \( - {2 \over 3} \) B: \( - {3 \over 4} \) C: \( - {1 \over 4} \) D: \( {1 \over 2} \)
- 向量组\({\alpha _1} = {\left( {1,1,1} \right)^T}{\kern 1pt} ,\;{\alpha _2} = {\left( {2,3,4} \right)^T},\,{\alpha _3} = {\left( {3,2,3} \right)^T},{\alpha _4} = {\left( {4,3,4} \right)^T}\)的一个极大无关组是( ) A: \({\alpha _1}\,,{\alpha _2}\) B: \({\alpha _1}\,,{\alpha _2},{\alpha _3}\) C: \({\alpha _2},{\alpha _3}\) D: \({\alpha _1}\,{\alpha _3}\)
- 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: \(2\)
- 向量组\(\left( {\matrix{ { - 1} \cr 3 \cr 1 \cr } } \right),\left( {\matrix{ 2 \cr 1 \cr 0 \cr } } \right),\left( {\matrix{ 1 \cr 4 \cr 1 \cr } } \right) \)线性相关.
- 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: \( 1 - {3^n} \)