Question

If A = [–1 a 2; 1 2 x; 3 1 1] and A⁻¹ = [1 –1 1; –8 7 –5; b y 3], find the value of (a + x) – (b + y).

If |–a b c; a –b c; a b –c| = kabc, then the value of k is :

Solve the following system of equations, using matrices : 2/x + 3/y + 10/z = 4, 4/x – 6/y + 5/z = 1, 6/x + 9/y – 20/z = 2 where x, y, z ≠ 0

If A = [1 cot x; –cot x 1], show that A′A⁻¹ = [–cos 2x –sin 2x; sin 2x –cos 2x].