Question

Let A = `[(2, 1),(0, -2)]`, B = `[(4, 1),(-3, -2)]` and C = `[(-3, 2),(-1, 4)]`. Find A² + AC – 5B.

Answer 1

Given: A = `[(2, 1),(0, -2)]`, B = `[(4, 1),(-3, -2)]` and C = `[(-3, 2),(-1, 4)]`

Now, 
A² = `[(2, 1),(0, -2)][(2, 1),(0, -2)]`

= `[(4 + 0, 2 - 2),(0 + 0, 0 + 4)]`

= `[(4, 0),(0, 4)]`

5B = `[(20, 5),(-15, -10)]`

AC = `[(2, 1),(0, -2)][(-3, 2),(-1, 4)]`

= `[(-6 - 1, 4 + 4),(0 + 2, 0 - 8)]`

= `[(-7, 8),(2, -8)]`

∴ A² + AC – 5B = `[(4, 0),(0, 4)] + [(-7, 8),(2, -8)] - [(20, 5),(-15, -10)]`

= `[(4 - 7 - 20, 0 + 8 - 5),(0 + 2 + 15, 4 - 8 + 10)]`

= `[(-23, 3),(17, 6)]`