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If A'=[[3,4],[ -1,2],[0, 1]]and B=[[-1, ...

If `A'=[[3,4],[ -1,2],[0, 1]]`and `B=[[-1, 2, 1],[1,2, 3]]`, then verify that `(A+B)^(prime)=A^(prime)+B^(prime)`

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Solvinf L.H.S `(A+B)'`
First finding `A+B`
Given
`A=(A')'=[[3,4],[ -1,2],[0, 1]]^'=[[3,-1,0],[4,2,1]]` and `B=[[-1, 2, 1],[1,2, 3]]`
Now,
`A+B=[[3,-1,0],[4,2,1]]+[[-1, 2, 1],[1,2, 3]]`

`A+B=[[3+(-1),-1+2,0+1],[4+1,2+2,1+3]]`
`A+B=[[2,1,1],[5,4,4]]`
So,
`(A+B)'=[[2,5],[1,4],[1,4]]`
Solving R.H.S
`(A'+B')`
Given `A'=[[3,4],[ -1,2],[0, 1]]`
Also,
`B=[[-1, 2, 1],[1,2, 3]]`
`therefore` `B'=[[-1,1],[2,2],[1,3]]`

`A'+B'=[[3,4],[ -1,2],[0, 1]]+[[-1,1],[2,2],[1,3]]=[[3+(-1),4+1],[-1+2,2+2],[0+1,1+3]]`

`A'+B'=[[2,5],[1,4],[1,4]]`= L.H.S
Hence, L.H.S=R.H.S
Hence Proved
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