x1+2x2+2x3+x4=0 (1) 2x1+x2-2x3-2x4=0 (2) x1-x2-4x3-3x4=0 (3)(2)-(3)x1+2x2+2x3+x4=0 = equation (1)rank of system of equations = 2(1)+(2)3x1+3x2+3x4=0x4=-(x1+x2)from (1)x1+2x2+2x3-(x1+x2)=0x3 = -x2/2sol...