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Let S_r be the 3x3 determinant | 2r x n(n+1) | | 6r²-1 y n²(2n+3) | | 4r³-2nr z n³(n+1) |. Then the sum S = sum_(r=1)ⁿ S_r is independent of which of the following?

1. x
2. y
3. n
4. all of these

Correct answer: all of these

Solution

Summing column 1 makes it proportional to column 3 (both become n(n+1), n²(2n+3)-type expressions), so the determinant sum S = 0, which is independent of x, y and n.

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