Computing an [[../02 Areas/Math/Augmented Matrix|Augmented Matrix]] with multiple [[Vector|Vectors]] on the right of the bar: $ \begin{array}{ccc} A=\mat{1&3\\-1&1\\1&1} & \vec b=\mat{2\\3\\0} & \vec c = \mat{1\\5\\-1} \end{array} \\ $ Solve for both $\vec x, \vec y \in \R^2$ $ \begin{align} A\vec x &= \vec b \\ A \vec y &= \vec c \end{align} $ $\begin{align} \mat{1&3\\-1&1\\1&1}\mat{\vec x & \vec y} &= \mat{2 & 1\\3&5\\0&-1} \\ \vdots\\ &\sim \augmented{cc|cc}{ 1&0&-1&-2\\ 0&1&1&1\\ 0&0&0&0 } \\ &\sim \begin{cases} x_{1}&=-1\\ x_{2}&=1\\ 0&=0 \\ y_{1}&=-2\\ y_{2}&=1\\ 0&=0\\ \end{cases} \end{align} $