What is the determinant of the coefficient matrix of the system? 4 x plus 3 y plus 2 z is equal to 0 negative 3 x plus y plus 5 z is equal to 0 negative x minus 4 y plus 3 z is equal to 0

The coefficient matrix is [[4, 3, 2], [-3, 1, 5], [-1, -4, 3]]. Expanding along the first row gives 4(1·3 − 5·(−4)) − 3((−3)·3 − 5·(−1)) + 2((−3)·(−4) − 1·(−1)) = 4(23) − 3(−4) + 2(13) = 130. The determinant is 130, choice A.

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