WAEC Mathematics 2017 Theory — Question 23

Model answer

MN = (1 2; 4 3)(m x; n y) = (m+2n, x+2y; 4m+3n, 4x+3y) = (2 1; 3 4). Equating elements: m+2n=2 ...(1); 4m+3n=3 ...(2); x+2y=1 ...(3); 4x+3y=4 ...(4). From (1): m=2-2n. Substituting into (2): 4(2-2n)+3n=3 → 8-8n+3n=3 → -5n=-5 → n=1, so m=0. From (3): x=1-2y. Substituting into (4): 4(1-2y)+3y=4 → 4-8y+3y=4 → -5y=0 → y=0, so x=1. Therefore N = (0 1; 1 0).