Question

20．已知矩阵A=$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$，B=$[\begin{array}{l}{3}\\{1}\end{array}]$满足AX=B，求矩阵X．

Answer 1

分析 设X=$[\begin{array}{l}{a}\\{b}\end{array}]$，由$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$$[\begin{array}{l}{a}\\{b}\end{array}]$=$[\begin{array}{l}{3}\\{1}\end{array}]$，由此能求X．

解答 解：设X=$[\begin{array}{l}{a}\\{b}\end{array}]$，
∵矩阵A=$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$，B=$[\begin{array}{l}{3}\\{1}\end{array}]$满足AX=B，
∴$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$$[\begin{array}{l}{a}\\{b}\end{array}]$=$[\begin{array}{l}{3}\\{1}\end{array}]$，∴$\left\{\begin{array}{l}{a+2b=3}\\{2a-b=1}\end{array}\right.$，…（6分）
解得$\left\{\begin{array}{l}{a=1}\\{b=1}\end{array}\right.$，解得X=$[\begin{array}{l}{1}\\{1}\end{array}]$．…（10分）

点评 本题考查矩阵的求法，是基础题，解题时要认真审题，注意矩阵运算法则的合理运用．