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in Matrices & determinants by (41.3k points)

If D = |(1, 1, 1), (1, 1 + x, 1), (1, 1, 1 + y)| for x ≠ 0, y ≠ 0 then D is 

(A) divisible by neither x nor y 

(B) divisible by both x and y

(C) divisible by x but not y

(D) divisible by y but not x

1 Answer

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Best answer

Answer is (B) divisible by both x and y

We have

Therefore, C2 → C2 - C1 and C3 → C3 - C1 and imply that

Hence, D is divisible by both x and y.

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