For a matrix A , A = a i j 3 × 3 ≠ 0 . If each element a i j is multiplied by k i - j , we obtain matrix B , such that α A + β B = 0, then the value of α + β is equal to

Step-by-step solution

Let, A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 , then B = a 11 a 12 k a 13 k 2 k a 21 a 22 a 23 k k 2 a 31 k a 32 a 33 B = a 11 a 12 k a 13 k 2 k a 21 a 22 a 23 k k 2 a 31 k a 32 a 33 B = 1 k 3 k 2 a 11 k a 12 a 13 k 2 a 21 k a 22 a 23 k 2 a 31 k a 32 a 33 = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 = A ⇒ - A + B = 0 On comparison, α + β = 0