Archetype C

Summary: System with three equations, four variables. Consistent. Null space of coefficient matrix has dimension 1.

Definition:\begin{align*} 2x_1 - 3x_2 + x_3 - 6x_4 &= -7 \\ 4x_1 +x_2 +2x_3 + 9x_4 &= -7 \\ 3x_1 +x_2 +x_3 + 8x_4 &= -8 \end{align*}