Let A = a i j 3 × 3 be a matrix such that a i j = i + 2 j 2 where i , j ∈ 1,3 and i , j ∈ N . If C i j be a cofactor of a i j , then the value of a 11 C 21 + a 12 C 22 + a 13 C 23 + a 21 C 31 + a 22 C 32 + a 33 C 33 + a 31 C 11 + a 32 C 12 + a 33 C 13 is equal to

Question

Let A = a i j 3 × 3 be a matrix such that a i j = i + 2 j 2 where i , j ∈ 1,3 and i , j ∈ N . If C i j be a cofactor of a i j , then the value of a 11 C 21 + a 12 C 22 + a 13 C 23 + a 21 C 31 + a 22 C 32 + a 33 C 33 + a 31 C 11 + a 32 C 12 + a 33 C 13 is equal to,

MARKS App · Accepted Answer

A = 3 2 5 2 7 2 2 3 4 5 2 7 2 9 2 ∵ Sum of the product of elements of any row to the corresponding cofactor of any other row is zero. a 11 C 21 + a 12 C 22 + a 13 C 23 = 0 a 21 C 31 + a 22 C 32 + a 23 C 33 = 0 a 32 C 12 + a 31 C 11 + a 33 C 13 = 0

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