3、若线性方程组的增广矩阵为 $\left(\begin{array}{lll}2 & 3 & c_{1} \\ 0 & 1 & c_{2}\end{array}\right)$ 、解为 $\left\{\begin{array}{l}x=3 \\ y=5\end{array}\right.$ ,则 $c_{1}-c_{2}=$ $\_\_\_\_$ .
参考答案16
2015_上海卷 (2015·理)
3、若线性方程组的增广矩阵为 $\left(\begin{array}{lll}2 & 3 & c_{1} \\ 0 & 1 & c_{2}\end{array}\right)$ 、解为 $\left\{\begin{array}{l}x=3 \\ y=5\end{array}\right.$ ,则 $c_{1}-c_{2}=$ $\_\_\_\_$ .
【答案】16
【解析】由题意得:$c_{1}=2 x+3 y=2 \times 3+3 \times 5=21, c_{2}=0 \cdot x+y=5, c_{1}-c_{2}=21-5=16$ .
【考点定位】线性方程组的增广矩阵