Question

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Evaluate the determinant of the matrix.
[[-4,5,6],[0,4,4],[-2,-5,4]]

Answer 1

To evaluate the determinant of the matrix, we can use the following formula for a 3x3 matrix:

det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)

Plugging in the values from our matrix:
a = -4, b = 5, c = 6
d = 0, e = 4, f = 4
g = -2, h = -5, i = 4

det(A) = -4(4*4 - (-5)*4) - 5(0*4 - (-2)*4) + 6(0*(-5) - 4*(-2))
det(A) = -4(16 + 20) - 5(0 + 8) + 6(0 + 8)
det(A) = -4(36) - 5(8) + 6(8)
det(A) = -144 - 40 + 48
det(A) = -136 + 48
det(A) = -88

Therefore, the determinant of the matrix [[-4,5,6],[0,4,4],[-2,-5,4]] is -88.