Question

1．線性方程組$\left\{\begin{array}{l}2x+4y-10=0\\ 3x=8y+2\end{array}\right.$的增廣矩陣是$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$．

Answer 1

分析 將線性方程組轉化成$\left\{\begin{array}{l}{2x+4y=10}\\{3x-8y=2}\end{array}\right.$，則$[\begin{array}{l}{2}&{4}\\{3}&{-8}\end{array}]$$[\begin{array}{l}{x}\\{y}\end{array}]$=$[\begin{array}{l}{10}\\{2}\end{array}]$，即可求得其增廣矩陣．

解答 解：由線性方程組：$\left\{\begin{array}{l}{2x+4y=10}\\{3x-8y=2}\end{array}\right.$，則$[\begin{array}{l}{2}&{4}\\{3}&{-8}\end{array}]$$[\begin{array}{l}{x}\\{y}\end{array}]$=$[\begin{array}{l}{10}\\{2}\end{array}]$，
∴其增廣矩陣為：$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$，
故答案為：$[\begin{array}{l}{2}&{4}&{10}\\{3}&{-8}&{2}\end{array}]$．

點評 本題考查線性方程組的應用，考查線性方程增廣矩陣的求法，考查計算能力，屬于基礎題．