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Find the value of x for which the matrix [[6,x],[7,-6]] is its own inverse.

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bleeeeee | Student | Honors

Posted April 7, 2013 at 3:54 AM via web

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Find the value of x for which the matrix [[6,x],[7,-6]] is its own inverse.

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pramodpandey | College Teacher | Valedictorian

Posted April 7, 2013 at 6:24 AM (Answer #1)

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`A=[[6,x],[7,-6]]` ,by given condition we need to determine x such that

`A.A=[[1,0],[0,1]]`

Substitute value of A

`[[6,x],[7,-6]][[6,x],[7,-6]]=[[1,0],[0,1]]`

`[[36+7x,0],[0,7x+36]]=[[1,0],[0,1]]`

`36+7x=1`

`7x=-35`

`x=-5`  

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