Question

2．已知矩阵M=$[\begin{array}{l}{2}&{1}\\{1}&{2}\end{array}]$，β=$[\begin{array}{l}{3}\\{5}\end{array}]$，计算M²β．

Answer 1

分析 通过M=$[\begin{array}{l}{2}&{1}\\{1}&{2}\end{array}]$可得M²=$[\begin{array}{l}{5}&{4}\\{4}&{5}\end{array}]$，进而可得M²β=$[\begin{array}{l}{35}\\{37}\end{array}]$．

解答 解：∵M=$[\begin{array}{l}{2}&{1}\\{1}&{2}\end{array}]$，∴M²=$[\begin{array}{l}{2}&{1}\\{1}&{2}\end{array}]$$[\begin{array}{l}{2}&{1}\\{1}&{2}\end{array}]$=$[\begin{array}{l}{5}&{4}\\{4}&{5}\end{array}]$，
又∵β=$[\begin{array}{l}{3}\\{5}\end{array}]$，∴M²β=$[\begin{array}{l}{5}&{4}\\{4}&{5}\end{array}]$$[\begin{array}{l}{3}\\{5}\end{array}]$=$[\begin{array}{l}{35}\\{37}\end{array}]$．

点评 本题考查矩阵的计算，注意解题方法的积累，属于基础题．