Question

4．設(shè)x為實(shí)數(shù)．若矩陣M=$[{\begin{array}{l}1&{-5}\\ 2&x\end{array}}]$為不可逆矩陣，求M²．

Answer 1

分析 由矩陣M為不可逆矩陣，|M|=0，求得x的值，根據(jù)矩陣的乘法求得M²．

解答 解：依題意，矩陣M=$[{\begin{array}{l}1&{-5}\\ 2&x\end{array}}]$為不可逆矩陣，
M的行列式|M|=0，解得：x=-10，
∴M²=$[{\begin{array}{l}1&{-5}\\ 2&{-10}\end{array}}][{\begin{array}{l}1&{-5}\\ 2&{-10}\end{array}}]=[{\begin{array}{l}{-9}&{45}\\{-18}&{90}\end{array}}]$，
M²=$[\begin{array}{l}{-9}&{45}\\{-18}&{90}\end{array}]$．

點(diǎn)評(píng) 本題考查矩陣可逆的條件，矩陣的乘法，屬于基礎(chǔ)題．