Solution RREF.C10 Robert Beezer

The augmented matrix row-reduces to \begin{equation*} \begin{bmatrix} \leading{1} & 0 & 0 & 0 & 1\\ 0 & \leading{1} & 0 & 0 & -3\\ 0 & 0 & \leading{1} & 0 & -4\\ 0 & 0 & 0 & \leading{1} & 1 \end{bmatrix} \end{equation*} This augmented matrix represents the linear system $x_1=1$, $x_2=-3$, $x_3=-4$, $x_4=1$, which clearly has only one possible solution. We can write this solution set then as \begin{align*} S&=\set{\colvector{1\\-3\\-4\\1}} \end{align*}