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Given the matrix A=[[x,3,2],[1,y,4],[2,2...

Given the matrix `A=[[x,3,2],[1,y,4],[2,2,z]]`. If `xyz=60 and 8x+4y+3z=20,` then `A(adjA)` is equal to

A

`[(64,0,0),(0,64,0),(0,0,64)]`

B

`[(88,0,0),(0,88,0),(0,0,88)]`

C

`[(68,0,0),(0,68,0),(0,0,68)]`

D

`[(34,0,0),(0,34,0),(0,0,34)]`

Text Solution

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The correct Answer is:
C
A adj. `A=|A| I`
`|A|=xyz-8x-3(z-8)+2(2-2y)`
`|A|=xyz-(8x+3z+4y)+28`
`=60-20+28=68`
`implies` A(adj. A)`=68 [(1,0,0),(0,1,0),(0,0,1)]=[(68,0,0),(0,68,0),(0,0,68)]`
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