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Let D be the determinant of the matrix | 1 1 1 | | 1 1+x 1 | | 1 1 1+y | where x ≠ 0 and y ≠ 0. Then D is

1. divisible by x, but not by y
2. divisible by y, but not by x
3. divisible by neither x nor y
4. divisible by both x and y

Correct answer: divisible by both x and y

Solution

The determinant D can be computed using properties of determinants and shows that it contains terms involving both x and y, indicating that it is divisible by both variables. This is due to the structure of the matrix, where the presence of x and y in the second and third rows leads to terms that include these variables when expanded.

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