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Question
If A = `[[2 -1],[3 2]]` and B = `[[0 4],[-1 7]]`find 3A2 − 2B + I
Solution
Given: A= `[[2 -1],[3 2]]`
Now,
`A^(2 )=A A`
`⇒ A^(2)=` `[[2 -1],[3 2]]` `[[2 -1],[3 2]]`
`⇒ A^(2)=[[4-3 - 2-2],[6+6 -3+4]]`
`⇒A^(2)=[[1 -4],[12 1]]`
`3A^(2)−2B+I`
`⇒3A^(2)−2B+I=3 [[1 -4],[12 1]]-2[[0 4],[-1 7]]+[[1 0],[0 1]]`
`⇒3A^(2)−2B+I=[[3 -12],[36 3]]-[[0 8],[-2 14]]+[[1 0],[0 1]]`
`⇒3A^(2)−2B+I=[[3-0+1 -12-8+0],[36+2+0 3-14+1]]`
`⇒3A^(2)−2B+I=[[4 -20],[38 -10]]`
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