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For the following matrices verify the ...

For the following matrices verify the distributivity of matrix multiplication over matrix addition i.e. `A(B+C)=A B+A C`
. (i)`A=[(1,-1),( 0 ,2)]` , `B=[(-1, 0),( 2 ,1)]` and `C=[(0, 1 ),(1,-1)]` (ii) `A=[(2,-1),( 1, 1),(-1, 2)]` , `B=[(0 ,1 ),(1 ,1)]` and `C=[(1,-1),( 0 ,1)]` .

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(i)Given that,
`A=[(1,-1),( 0 ,2)]`
, `B=[(-1, 0),( 2 ,1)]`
and `C=[(0, 1 ),(1,-1)]`
`(LHS)=A(B+C)`
`=[(1,-1),( 0 ,2)]([(-1, 0),( 2 ,1)]+[(0, 1 ),(1,-1)])`
`=[(1,-1),( 0 ,2)][(-1,1),(3,0)]`
`=[(-4,1),(6,0)]`
`text(RHS)=AB+AC`
`=[(1,-1),( 0 ,2)][(-1, 0),( 2 ,1)]+[(1,-1),( 0 ,2)][(0, 1 ),(1,-1)]`
`=[(-3,-1),(4,2)]+[(-1,2),(2,-2)]`
`=[(-4,1),(6,0)]`
hence `A(B+C)=A B+A C`
(ii) Given that,
`A=[(2,-1),( 1, 1),(-1, 2)]`
, `B=[(0 ,1 ),(1 ,1)]`
and `C=[(1,-1),( 0 ,1)]`
`text(LHS)=A(B+C)`
`=[(2,-1),( 1, 1),(-1, 2)]([(0 ,1 ),(1 ,1)]+[(1,-1),( 0 ,1)])`
`=[(2,-1),( 1, 1),(-1, 2)][(1,0),(1,2)]`
`=[(1,-2),(2,2),(1,4)]`
`(RHS)=AB+AC`
`=[(2,-1),( 1, 1),(-1, 2)][(0 ,1 ),(1 ,1)]+[(2,-1),( 1, 1),(-1, 2)][(1,-1),( 0 ,1)]`
`=[(-1,1),(1,2),(2,1)]+[(2,-3),(1,0),(-1,3)]`
`=[(1,-2),(2,2),(1,4)]`
hence `A(B+C)=A B+A C`
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