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If P=[(1,alpha,3),(1,3,3),(2,4,4)] is t...

If `P=[(1,alpha,3),(1,3,3),(2,4,4)]` is the adjoint of a 3 x 3 matrix A and `|A| = 4`, then `alpha` is equal to

A

11

B

5

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Given, adj A = P
`therefore abs("adj "A) = abs(P)`
` rArr abs(A)^(3-1) = abs(P) " "[because abs(A)=A]`
`rArr 16 = abs(P)`
`rArr 16 = abs((1,alpha,3),(1,3,3),(2,4,4))`
`rArr 16 = 1(0) - alpha (4-6) + 3(4-6) `
`rArr 16 = a alpha -6`
`rArr 2 alpha = 22`
`therefore alpha = 11`
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