Summary: Linear system of three equations, three unknowns. Singular coefficient matrix with dimension 1 null space. Integer eigenvalues and a degenerate eigenspace for coefficient matrix.
Definition:\begin{align*} x_1 -x_2 +2x_3 & =1\\ 2x_1+ x_2 + x_3 & =8\\ x_1 + x_2 & =5 \end{align*}