What is the determinant of the coefficient matrix of the system? negative 3 x plus 2 y minus 6 z is equal to 5 negative 7 x plus 9 y minus 1 z is equal to 4 negative 2 x plus 5 y plus 2 z is equal to 9

The coefficient matrix is [[-3, 2, -6], [-7, 9, -1], [-2, 5, 2]]. Expanding along the first row gives -3(9·2 - (-1)·5) - 2((-7)·2 - (-1)(-2)) + (-6)((-7)·5 - 9(-2)) = -69 + 32 + 102 = 65. The determinant is 65, so the correct choice is B, 65.

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