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The number of real values of x for which the determinant of the matrix with rows (x, 3x+2, 2x-1), (2x-1, 4x, 3x+1), (7x-2, 17x+6, 12x-1) equals 0 is:
- 3
- 0
- 1
- infinite
Correct answer: infinite
Solution
Row 3 equals 3 times Row 1 plus 2 times Row 2 for every x, so the rows are always linearly dependent and the determinant is identically zero, giving infinitely many solutions.
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