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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

`64I`

B

`88I`

C

`68I`

D

`34I`

Text Solution

Verified by Experts

The correct Answer is:
C
`because A ("adj "A) = abs(A) I`
Now, `abs (A) = abs((3,3,2),(1,y,4),(2,2,z))`
`= x(yz-8) - 3 (z-8) + 2(2-2y)`
`= xyz - (8x+4y+3z)+28`
`=60 - 20 + 28 = 68 `
From Eq. (i), A (adj A) `= 68 I`
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