Question

1．线性方程组$\left\{\begin{array}{l}2x+4y-10=0\\ 3x=8y+2\end{array}\right.$的增广矩阵是$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$．

Answer 1

分析 将线性方程组转化成$\left\{\begin{array}{l}{2x+4y=10}\\{3x-8y=2}\end{array}\right.$，则$[\begin{array}{l}{2}&{4}\\{3}&{-8}\end{array}]$$[\begin{array}{l}{x}\\{y}\end{array}]$=$[\begin{array}{l}{10}\\{2}\end{array}]$，即可求得其增广矩阵．

解答 解：由线性方程组：$\left\{\begin{array}{l}{2x+4y=10}\\{3x-8y=2}\end{array}\right.$，则$[\begin{array}{l}{2}&{4}\\{3}&{-8}\end{array}]$$[\begin{array}{l}{x}\\{y}\end{array}]$=$[\begin{array}{l}{10}\\{2}\end{array}]$，
∴其增广矩阵为：$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$，
故答案为：$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$．

点评 本题考查线性方程组的应用，考查线性方程增广矩阵的求法，考查计算能力，属于基础题．