Question

10．若线性方程组的增广矩阵为$（\begin{array}{l}{a}&{0}&{2}\\{0}&{1}&{b}\end{array}）$，解为$\left\{{\begin{array}{l}{x=2}\\{y=1}\end{array}}\right.$，则a+b=2．

Answer 1

分析 根据增广矩阵的定义得到$\left\{{\begin{array}{l}{x=2}\\{y=1}\end{array}}\right.$是方程组$\left\{\begin{array}{l}{ax=2}\\{y=b}\end{array}\right.$的解，解方程组即可．

解答 解：由题意知$\left\{{\begin{array}{l}{x=2}\\{y=1}\end{array}}\right.$是方程组$\left\{\begin{array}{l}{ax=2}\\{y=b}\end{array}\right.$的解，
即$\left\{\begin{array}{l}{2a=2}\\{1=b}\end{array}\right.$，
则a+b=1+1=2，
故答案为：2．

点评 本题主要考查增广矩阵的求解，根据条件建立方程组关系是解决本题的关键．