Evaluate the determinant of the matrix.$\begin{vmatrix}-2&7&0\\-3&1&4\\5&0&-6\end{vmatrix}=$|−2 7 0−3 1 45 0 −6|=​

To calculate the determinant of a 3x3 matrix, we can use the formula:

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

where: a, b, c are the entries of the first row, d, e, f are the entries of the second row, g, h, i are the entries of the third row.

For the given matrix, we have:

a = -2, b = 7, c = 0, d = -3, e = 1, f = 4, g = 5, h = 0, i = -6.

Substituting these values into the formula, we get:

det(A) = -2(1*(-6) - 40) - 7(-3(-6) - 45) + 0(-30 - 1*5) = -2(-6) - 7(-18 - 20) + 0 = 12 - 7(-38) + 0 = 12 + 266 = 278

So, the determinant of the given matrix is 278.