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

Question

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

Given the matrix `A = [[x,3,2],[1,y,4],[2,2,z]]cdot` If `xyz = 60` and
`8x + 4y + 3z = 20, ` then `A(adjA)` is equal to
A. `64I`
B. `88I`
C. `68I`
D. `34I`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29