If D = 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y for x ≠ 0, y ≠ 0 , then D is: - Mathematics MCQ AIEEE 2007 2026 | ExamTest.live

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If D = 111 1 1 + x 1 11 1 + y for x \neq = 0, y \neq = 0, then D is:

Solution & Step-by-step Explanation

Applying row operations R_{2} \to R_{2} - R_{1} and R_{3} \to R_{3} - R_{1} : D = 100 1 x 0 10 y Expanding along the first column: D = 1 (x y - 0) = x y Since D = x y, it is divisible by both x and y .

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If D = 111 1 1 + x 1 11 1 + y for x \neq = 0, y \neq = 0, then D is:

divisible by neither x nor y

divisible by both x and y

divisible by x but not y

divisible by y but not x

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