Solution RREF.C11 Robert Beezer

The augmented matrix row-reduces to \begin{equation*} \begin{bmatrix} \leading{1} & 0 & 1 & 4/5 & 0\\ 0 & \leading{1} & -1 & -1/10 & 0\\ 0 & 0 & 0 & 0 & \leading{1} \end{bmatrix} \end{equation*} Row 3 represents the equation $0=1$, which is patently false, so the original system has no solutions. We can express the solution set as the empty set, $\emptyset=\set{\ }$.