第 1 题
1 分Given the matrix \( M = \begin{pmatrix} k & 2 \\ 3 & 4 \end{pmatrix} \), find the value of \( k \) such that the determinant of \( M \) is zero.
Pearson Edexcel International A Level · Further Mathematics (YFM01)
矩陣代數綜合：练习题
5 道选择题即时批改，另有 3 道文字题附完整解题步骤，全部围绕「矩陣代數綜合」。
8 道题目14 分免费，无需注册
第 2 题
1 分If \( AB = C \), where \( A = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix} \) and \( C = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix} \), find the matrix \( B \).
第 3 题
1 分The matrix \( N = \begin{pmatrix} a-2 & 4 \\ 3 & a+2 \end{pmatrix} \) is singular. Determine the two possible values of the real constant \( a \).
第 4 题
1 分Find the determinant of the matrix \( A = \begin{pmatrix} 4 & -2 \\ 5 & 3 \end{pmatrix} \).
第 5 题
1 分Given the matrices \( A = \begin{pmatrix} 2 & 1 \\ -1 & 3 \end{pmatrix} \) and \( B = \begin{pmatrix} 0 & 2 \\ 4 & -1 \end{pmatrix} \), calculate the matrix product \( AB \).
第 6 题
2 分Calculate the determinant of the matrix \( \mathbf{A} = \begin{pmatrix} 4 & -2 \\ 3 & 5 \end{pmatrix} \).
先自己写一遍答案，再对照解题步骤。
第 7 题
4 分Find the value of the constant \( k \) for which the matrix \( \mathbf{M} = \begin{pmatrix} k & 4 \\ 3 & k-1 \end{pmatrix} \) is singular.
先自己写一遍答案，再对照解题步骤。
第 8 题
3 分The matrix \( {M} \) is defined by \( {M} = \begin{pmatrix} k & 2 \\ 3 & k-1 \end{pmatrix} \), where \(k\) is a real constant.
(a) Find the values of \(k\) for which \( {M} \) is a singular matrix.
(b) Given that \(k = 4\), find \( {M}^{-1} \).
先自己写一遍答案，再对照解题步骤。
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