Given the matrices a and B as `A=[(1,-1),(4,-1)]` and `B=[(1,-1),(2,-2)]`. The two matrices X and Y are such that `XA=B` and `AY=B`, then find the mat

Question

Given the matrices a and B as `A=[(1,-1),(4,-1)]` and `B=[(1,-1),(2,-2)]`. The two matrices X and Y are such that `XA=B` and `AY=B`, then find the mat

Given the matrices a and B as `A=[(1,-1),(4,-1)]` and `B=[(1,-1),(2,-2)]`. The two matrices X and Y are such that `XA=B` and `AY=B`, then find the matrix `3(X+Y)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Here a is non singular but b is singular hence only `A^(-1)` exists
Now `XA=B`
or `X=BA^(-1)` (1)
And `AY=B`
or `Y=A^(-1)B` (2)
Also `A^(-1)=1/3 [(-1,1),(-4,1)]`
`implies X=BA^(-1)=1/3 [(1,-1),(2,-2)][(-1,1),(-4,1)]=[(1,0),(2,0)]`
`implies Y=A^(-1) B=1/3 [(-1,1),(-4,1)][(1,-1),(2,-2)]=1/3 [(1,-1),(-2,2)]`
`implies 3(X+Y) =[(3,0),(6,0)]+[(1,-1),(-2,2)]=[(4,-1),(4,2)]`