题目 Problem Given that A=(1k2−1)andB=(30−22k)\mathbf{A} = \begin{pmatrix} 1 & k \\ 2 & -1 \end{pmatrix} \quad \text{and} \quad \mathbf{B} = \begin{pmatrix} 3 & 0 \\ -2 & 2k \end{pmatrix}A=(12k−1)andB=(3−202k) where kkk is a non-zero constant, (a) determine the matrix AB\mathbf{AB}AB (2) (b) determine the value of kkk for which det(AB)=0\det(\mathbf{AB}) = 0det(AB)=0 (3) 题目中文翻译 已知 A=(1k2−1)和B=(30−22k)\mathbf{A} = \begin{pmatrix} 1 & k \\ 2 & -1 \end{pmatrix} \quad \text{和} \quad \mathbf{B} = \begin{pmatrix} 3 & 0 \\ -2 & 2k \end{pmatrix}A=(12k−1)和B=(3−202k) 其中 kkk 为非零常数， (a) 求矩阵 AB\mathbf{AB}AB (b) 求使 det(AB)=0\det(\mathbf{AB}) = 0det(AB)=0 的 kkk 值 解答
