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If Aprime=[[-2, 3],[ 1, 2]]and B=[[-1, 0...

If `Aprime=[[-2, 3],[ 1, 2]]`and `B=[[-1, 0],[ 1, 2]]`, then find `(A+2B)^(prime)`.

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We need to find `(A+2B)^(prime)`
Finding A
`A'=[[-2, 3],[ 1, 2]]`
`A=(A')'=[[-2,1],[3,2]]`
Also,
`B=[[-1, 0],[ 1, 2]]`
`2B=2[[-1,0],[1,2]]=[[2(-1),2(0)],[2(1),2(2)]]`
`2B=[[-2,0],[2,4]]`
Now
`A+2B=[[-2,1],[3,2]]+[[-2,0],[2,4]]`
`A+2B=[[-2+(-2),1+0],[3+2,2+4]]`
`A+2B=[[-4,1],[5,6]]`

`therefore` `(A+2B)'=[[-4,5],[1,6]]`.
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