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