What is the determinant of the coefficient matrix of the system? negative x minus y plus 2 z is equal to 5 3 x plus 2 y minus z is equal to 3 4 x plus 4 y minus 8 z is equal to negative 2

The coefficient matrix is [[-1, -1, 2], [3, 2, -1], [4, 4, -8]]. Its third row is −4 times its first row, so the rows are linearly dependent. A matrix with linearly dependent rows has determinant 0, so the correct choice is C, 0.

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