Question

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. 4
B. 11
C. 5
D. 0

Answer 1

Given, `P =|{:(1, alpha, 3), (1, 3, 3),(2, 4, 4):}|`
`therefore |P| = 1(12-12)-alpha(4-6) + 3 (4-6) = 2 alpha -6`
`because "P = adj"(A) " " ["given"]`
`therefore |P| =|adj A| = |A|^(2) = 16 " " [because|adj A| = |A|^(n-1)]`
`therefore 2 alpha-6 = 16`
`rArr 2 alpha = 22`
`rArr alpha = 11`