Let the determinant of a square matrix A of order m be m - n , where m and n satisfy 4 m + n = 22 and 17 m + 4 n = 93 . If d e t n a d j a d j m A = 3 a 5 b 6 c , then a + b + c is equal to

Step-by-step solution

We have been given that A = m - n , where 4 m + n = 22   . . . . . . . i and 17 m + 4 n = 93   . . . . . . . ii Solving i and ii m = 5 ,   n = 2 Order = 5 ⇒ A = 3 We know that a d j A = A w - 1 a d j a d j A = A w - 1 2   where w × w is the order of the matrix. ∴   d e t   n   a d j   a d j m A = 2 a d j   a d j   5 A = 2 5 5 A 16 = 2 5   5 80   A 16 = 2 5 · 3 16 · 5 80 = 3 11   5 80   6 5 So, a + b + c = 96 Hence this