Let matrix A = x y - z 1 2 3 1 1 2 , where x , y , z ∈ N . If adj adj adj adjA = 4 8 · 5 16 , then the number of such matrices A is equal to (where, M represents determinant of a matrix M )

Question

Let matrix A = x y - z 1 2 3 1 1 2 , where x , y , z ∈ N . If adj adj adj adjA = 4 8 · 5 16 , then the number of such matrices A is equal to (where, M represents determinant of a matrix M ),

MARKS App · Accepted Answer

d e t . a d j a d j a d j a d j A = A 3 - 1 4 = A 16 = 4 8 . 5 16 ⇒ A = ± 10 A = x y - z 1 2 3 1 1 2 = x + y + z = ± 10 ∵ x , y , z ∈ N ⇒ x + y + z = - 10 (not possible) Hence, x + y + z = 10 The number of such matrices = 9 C 2 = 3 6

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