Question

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

Answer 1

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

解答 解：設(shè)X=$[\begin{array}{l}{a}\\\end{array}]$，
∵矩陣A=$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$，B=$[\begin{array}{l}{3}\\{1}\end{array}]$滿足AX=B，
∴$[\begin{array}{l}{1}&{2}\\{2}&{-1}\end{array}]$$[\begin{array}{l}{a}\\\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）

點(diǎn)評(píng) 本題考查矩陣的求法，是基礎(chǔ)題，解題時(shí)要認(rèn)真審題，注意矩陣運(yùn)算法則的合理運(yùn)用．