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Solution for Find the inverse of the matrix, A=[[1,3,3],[1,4,3],[1,3,4]] by using column transformations. - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

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Question

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

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 C1 → C1 - C3

`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]]`

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 2014-2015 (October) (with solutions)
Question 2.2.1 | 4.00 marks

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Solution for question: Find the inverse of the matrix, A=[[1,3,3],[1,4,3],[1,3,4]] by using column transformations. concept: Elementary Operation (Transformation) of a Matrix. For the courses HSC Science (Electronics), HSC Science (General) , HSC Arts, HSC Science (Computer Science)
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