Let ( A = [ a _ i j ]= [ array cc ₅ 128 & ₄ 5 ₅ 8 & ₄ 25 array ] ). If ( A _ i j ) is the cofactor of ( a _ i j , C _ i j = _ k =1 ^2 a _ i k A _ j k , 1 i, j 2 ), and ( C = [ C _ i j ] ), then (8| C | ) is equal to :

Step-by-step solution

aligned & | A |= 11 2 & C ₁₁= _ k =1 ^2 a _ 1 k A _ 1 k = a ₁₁ ~A ₁₁+ a ₁₂ ~A ₁₂=| A |= 11 2 & C ₁₂= _ k =1 ^2 a _ 1 k A _ 2 k =0 & C ₂₁= _ k =1 ^2 a _ 2 k A _ 1 k =0 & C ₂₂= _ k =1 ^2 a _ 2 k A _ 2 k =| A |= 11 2 & C = [ array cc 11 / 2 & 0 0 & 11 / 2 array ] & | C |= 121 4 & 8| C |=242 aligned