矩阵(A=egin{bmatrix}1&2&-1 \ 3&4&-3\ 5&-4&1 end{bmatrix})可逆.
举一反三
- 设`alpha_{1}, alpha_{2},alpha_{3}`均为3维列向量,记矩阵(A=egin{bmatrix}alpha_{1} ,& alpha_{2} ,& alpha_{3}end{bmatrix}),(B=egin{bmatrix}alpha_{1}+alpha_{2}+alpha_{3} , & alpha_{1}+2alpha_{2}+4alpha_{3} , & alpha_{1}+3alpha_{2}+9alpha_{3} end{bmatrix},) 如果(egin{vmatrix} A end{vmatrix}=1,)那么(egin{vmatrix} B end{vmatrix})=______
- 已知矩阵(A=egin{bmatrix} 1&2 &3 \4 &5 &6 end{bmatrix}),若对A做初等变换,可将矩阵A化为单位阵.
- 设矩阵\(N=\begin{bmatrix} 0 & A \\ B & 0 \end{bmatrix}\),其中\(A=\begin{bmatrix}4 & 1 \\ 3& 1\end{bmatrix}\),\(B=\begin{bmatrix}1 & 0 \\ 0& 1\end{bmatrix}\),则\(N^{-1}=\)
- 求下面矩阵的 Cholesky 分解 (다음 행렬의 Cholesky factorization을 구하시오). \begin{bmatrix}<br/>1\ \,\, 3\ \,\, 7\\ <br/>3\ 10\ 26\\ <br/>7\ 26\ 75\\<br/>\end{bmatrix} A: \(U=\begin{bmatrix}<br/>1\ 3\ 7\\ <br/>0\ 1\ 5\\ <br/>0\ 0\ 1\\<br/>\end{bmatrix}\) B: \(U=\begin{bmatrix}<br/>1\ 2\ 7\\ <br/>0\ 3\ 5\\ <br/>0\ 0\ 1\\<br/>\end{bmatrix}\) C: \(U=\begin{bmatrix}<br/>1\ 3\ 7\\ <br/>0\ 2\ 5\\ <br/>0\ 0\ 1\\<br/>\end{bmatrix}\) D: \(U=\begin{bmatrix}<br/>1\ 3\ 1\\ <br/>0\ 1\ 5\\ <br/>0\ 0\ 7\\<br/>\end{bmatrix}\) E: \(U=\begin{bmatrix}<br/>1\ 2\ 7\\ <br/>0\ 3\ 1\\ <br/>0\ 0\ 1\\<br/>\end{bmatrix}\)
- \(二次型f(x)=x^{T}\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}x的秩为\)