Question

If A = `[(3 , 1),(-1 , 2)]` and I = `[(1 , 0),(0, 1)]`
find A² - 5A + 7 I.

Answer 1

A² = A · A
= `[(3 , 1),(-1 , 2)][(3 , 1),(-1 , 2)]`
= `[(9 - 1, 3 + 2),(-3 -2, -1 + 4)]`
= `[(8, 5),(-5, 3)]`
⇒A² - 5A + 71
= `[(8, 5),(-5, 3)] -5[(3 , 1),(-1 , 2)] +7 [(1 , 0),(0 , 1)]`
= `[(8, 5),(-5, 3)] - [(15 , 5),(-5, 10)] + [(7 , 0),(0 , 7)]`
= `[(-7 , 0),(0 , -7)] + [(7 , 0),(0 , 7)]`
= `[(0 , 0),(0 , 0)]`
= 0