Let A = a i j 3 × 3 be a matrix, where a i j = x i ≠ j 1 i = j ∀ i , j ∈ N & i , j ≤ 3 . If C i j be the cofactor of a i j and C 12 + C 23 + C 32 = 6 , then the number of value(s) of x ∀ x ∈ R is(are)

Question

Let A = a i j 3 × 3 be a matrix, where a i j = x i ≠ j 1 i = j ∀ i , j ∈ N & i , j ≤ 3 . If C i j be the cofactor of a i j and C 12 + C 23 + C 32 = 6 , then the number of value(s) of x ∀ x ∈ R is(are),

MARKS App · Accepted Answer

A = 1 x x x 1 x x x 1 C 12 = x 2 - x C 23 = x 2 - x C 32 = x 2 - x C 12 + C 23 + C 32 = 6 3 x 2 - x = 6 x 2 - x - 2 = 0 x = 2 , - 1

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