x0 + x2 + 2x3 = 2 (mod 3) 2x0 + 2x1 + x3 = 0 (mod 3) x1 + x2 + 2x4 = 0 (mod 3) 2x0 + 2x2 + x4 = 0 (mod 3) x1 + x3 + 2x4 = 2 (mod 3) after elementary row manipulation 1 0 1 2 0 0 2 1 0 0 0 0 2 0 2 0 0 0 2 1 0 0 0 0 2 hence, full rank. Unique solution: x0 = 1 x1 = 1 x2 = 0 x3 = 2 x4 = 1