Evaluate the determinant of the matrix.$\begin{vmatrix}6&1&2\\5&0&4\\9&3&0\end{vmatrix}=$|6 1 25 0 49 3 0|=​

It seems like there's a mistake in your question. The matrix you provided is a 3x3 matrix, but the determinant calculation you started seems to be for a 4x4 matrix.

Let's calculate the determinant for the 3x3 matrix you provided:

$\begin{vmatrix}6&1&2\\5&0&4\\9&3&0\end{vmatrix}$

We can use the formula for the determinant of a 3x3 matrix:

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

So in this case:

a = 6, b = 1, c = 2 d = 5, e = 0, f = 4 g = 9, h = 3, i = 0

Substituting these values into the formula gives:

det(A) = 6(00 - 43) - 1(50 - 49) + 2(53 - 09) = 6(-12) - 1(-36) + 2(15) = -72 + 36 + 30 = -6

So, the determinant of the matrix is -6.