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If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1...

If `A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),(13),(9)]`, and `CB=D`. Solve the equation `AX=B`.

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Verified by Experts

The correct Answer is:
`X=[(1),(-1),(1)]`
Given that `CB=D`. Now,
`AX=B`
or `CAX=CB=D`
or `X=(CA)^(-1)D`
Now, `CA=[(2,1,1),(2,2,1),(1,1,1)][(1,2,2),(2,2,3),(1,-1,3)]=[(5,5,10),(7,7,13),(4,3,8)]`
and `(CA)^(-1)=[(-17/5,2,1),(4/5,0,-1),(7/5,-1,0)]`
`implies (CA)^(-1) D=[(-17/5,2,1),(4/5,0,-1),(7/5,-1,0)][(10),(13),(9)]=[(1),(-1),(1)]`
`implies X=[(1),(-1),(1)]`
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CENGAGE-MATRICES-Exercise 13.5
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