Question

14．已知矩阵A=$[\begin{array}{l}{1}&{-2}\\{-2}&{-1}\end{array}]$，B=$[\begin{array}{l}{5}\\{-15}\end{array}]$满足AX=B，求矩阵X．

Answer 1

分析 由AX=B，得$[\begin{array}{l}{1}&{-2}\\{-2}&{-1}\end{array}]$$[\begin{array}{l}{a}\\{b}\end{array}]$=$[\begin{array}{l}{5}\\{-15}\end{array}]$，求解即可．

解答 解：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}{5}\\{-15}\end{array}]$
得$\left\{\begin{array}{l}{a-2b=5}\\{-2a-b=-15}\end{array}\right.$解得$\left\{\begin{array}{l}{a=7}\\{b=1}\end{array}\right.$
此时x=$[\begin{array}{l}{7}\\{1}\end{array}]$

点评 本题主要考查了矩阵的应用，属于基础题型．