Consider a matrix A = a i j 3 × 3 where, a i j = i + 2 j ∀ i j = e v e n 2 i - 3 j ∀ i j = o d d . If b i j is the cofactor of a i j in matrix A and C i j = ∑ r = 1 3 a i r b j r , then C i j 3 × 3 is

Step-by-step solution

A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 = - 1 5 - 7 4 6 8 3 7 - 3 B = b 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 A = - 1 - 18 - 56 - 5 - 12 - 24 - 7 28 - 18 = 184 C i j = a i 1 b j 1 + a i 2 b j 2 + a i 3 b j 3 C 11 = a 11 b 11 + a 12 b 12 + a 13 b 13 = A C 12 = a 11 b 21 + a 12 b 22 + a 13 b 23 = 0 Similarly, C 13 = 0 , C 21 = 0 , C 22 = A , C 23 = 0 , C 31 = 0 C 32 = 0 , C 33 = A C i j 3 × 3 = A 0 0 0 A 0 0 0 A = 184 0 0 0 184 0 0 0 184