Question

if A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`, find AC + B² – 10C.

Answer 1

A = `[(2,3),(5,7)]`, B = `[(0,4),(-1,7)]` and c = `[(1,0),(-1, 4)]`

Now, AC  = A x C = `[(2,3),(5,7)] xx [(1,0),(-1,4)]`

`= [(2xx1+3xx(-1), 2xx0+3xx4), (5xx1+7xx(-1),5xx0+7xx4)]`

`= [(2-3, 0+12),(5-7, 0+28)]`

`= [(-1,12),(-2, 28)]`

And B² = B X B = `[(0,4),(-1,7)]xx[(0,4),(-1,7)]`

`= [(0xx0+4xx(-1), 0xx4+4xx7),(-1xx0+7xx(-1), -1xx4+7xx7)]`

`= [(0-4,0+28),(0-7,-4+49)]`

`= [(-4,28),(-7,45)]`

Now, AC + B² - 10C = `[(-1,12),(-2,28)] + [(-4,28),(-7,45)] - 10[(1,0),(-1,4)]`

`= [(-1,12),(-2,28)] + [(-4,28),(-7,45)] - [(10,0),(-10,40)]`

`= [(-1-4-10, 12+28-0),(-2-7+10, 28+45-40)]`

`= [(-15,40),(1,33)]`