Question

15．已知矩阵A=$[\begin{array}{l}1-2\\ 3-5\end{array}]$，若矩阵Z满足A^-1Z=$[\begin{array}{l}1\\ 1\end{array}]$，试求矩阵Z．

Answer 1

分析 由矩阵的运算法则Z=A$[\begin{array}{l}1\\ 1\end{array}]$=$[\begin{array}{l}{-1}\\{-2}\end{array}]$，即可求得Z．

解答 解：A=$|\begin{array}{l}{1}&{-2}\\{3}&{-5}\end{array}|$=-5+6=1≠0，
A可逆，
A^-1Z=$[\begin{array}{l}1\\ 1\end{array}]$，
∴Z=A$[\begin{array}{l}1\\ 1\end{array}]$=$[\begin{array}{l}1-2\\ 3-5\end{array}]$$[\begin{array}{l}1\\ 1\end{array}]$=$[\begin{array}{l}{-1}\\{-2}\end{array}]$，
∴Z=$[\begin{array}{l}{-1}\\{-2}\end{array}]$．

点评 本题考查矩阵的运算，考查逆矩阵的意义，考查计算能力，属于基础题．