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Find the Inverse of the Matrix, A= (1,3,3),(1,4,3),(1,3,4) by Using Column Transformations. - Mathematics and Statistics

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Sum

Find the inverse of the matrix,  `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.

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Solution

`A=[[1,3,3],[1,4,3],[1,3,4]]`

`|A|=|[1,3,3],[1,4,3],[1,3,4]|`

`=1(16-9)-3(4-3)+3(3-4)`

=1 ≠ 0

A-1  Exists

consider A-1A=I

`A^-1[[1,3,3],[1,4,3],[1,3,4]]=[[1,0,0],[0,1,0],[0,0,1]]`

Applying C2 → C2 -3C1 and C3→ C3 - 3C1,

`A^-1[[1,0,0],[1,1,0],[1,0,1]]=[[1,-3,-3],[0,1,0],[0,0,1]]`

Applying C1→  C1 - C2,

`A^-1[[1,0,0],[0,1,0],[1,0,1]]=[[4,-3,-3],[-1,1,0],[0,0,1]]`

Applying C3 → C3 - C1

`A^-1[[1,0,0],[0,1,0],[0,0,1]]=[[7,-3,-3],[-1,1,0],[-1,0,1]]`

`A^-1=[[7,-3,-3],[-1,1,0],[-1,0,1]]`

Concept: Elementary Transformations
  Is there an error in this question or solution?

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