Question

15．在平面直角坐标系xOy中，设点P（x，3）在矩阵M=$[{\begin{array}{l}1&2\\ 3&4\end{array}}]$对应的变换下得到点Q（y-4，y+2），求M²$[{\begin{array}{l}x\\ y\end{array}}]$．

Answer 1

分析 利用矩阵变换，求出x，y，再利用矩阵变换，即可求M²$[{\begin{array}{l}x\\ y\end{array}}]$．

解答 解：由题意，$[\begin{array}{l}{y-4}\\{y+2}\end{array}]$=$[{\begin{array}{l}1&2\\ 3&4\end{array}}]$$[\begin{array}{l}{x}\\{3}\end{array}]$，
∴$\left\{\begin{array}{l}{x+6=y-4}\\{3x+12=y+2}\end{array}\right.$，∴x=0，y=10，
$[{\begin{array}{l}1&2\\ 3&4\end{array}}]$$[{\begin{array}{l}1&2\\ 3&4\end{array}}]$=$[\begin{array}{l}{7}&{10}\\{15}&{22}\end{array}]$，
∴M²$[{\begin{array}{l}x\\ y\end{array}}]$=$[\begin{array}{l}{7}&{10}\\{15}&{22}\end{array}]$$[\begin{array}{l}{0}\\{10}\end{array}]$=$[\begin{array}{l}{100}\\{220}\end{array}]$．

点评 本题考查矩阵与变换，考查学生的计算能力，属于中档题．