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Let [a] denote the greatest integer not exceeding a. Given -1 <= x < 0, 0 <= y < 1, and 1 <= z < 2, evaluate the 3x3 determinant whose rows are ([x]+1, [y], [z]), ([x], [y]+1, [z]), and ([x], [y], [z]+1).

1. [x]
2. [y]
3. [z]
4. none of these

Correct answer: [z]

Solution

For a matrix [[a+1,b,c],[a,b+1,c],[a,b,c+1]], the determinant simplifies to a + b + c + 1. Substitute a=[x]=-1, b=[y]=0, c=[z]=1.

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