Question

If A = `[(3, -5),(-4, 2)]` find A² – 5A – 14I
Where I is unit matrix of order 2 x 2

Answer 1

Given
A = `[(3, -5),(-4, 2)]` 
A² = A x A = `[(3, -5),(-4, 2)][(3, -5),(-4, 2)]`

= `[(9 + 20, -15 - 10),(-12 - 8, 20 + 4)]`

= `[(29, -25),(-20, 24)]`

5A = `5[(3, -5),(-4, 2)]`

= `[(15, -25),(-20, 10)]`

∴ A² – 5A – 14 I = `[(29, -25),(-20, 24)]`

`-[(15, -25),(-20, 10)] -14[(1, 0),(0, 1)]`

= `[(29, -25),(-20, 24)] - [(15, -20),(-20, 10)] - [(14, 0),(0, 1)]`

= `[(29 - 15 - 14, -25 + 25 - 0),(-20 + 20 + 0, 24 - 10 - 14)]`

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