Evaluate the determinant of the matrix.$\begin{vmatrix}2&-1&3\\5&0&7\\0&-6&-4\end{vmatrix}=$|2 −1 35 0 70 −6 −4|=​

To calculate the determinant of a 3x3 matrix, we can use the rule of Sarrus.

First, we write down the matrix and copy the first two columns to the right of the matrix:

2 -1 3 2 -1 5 0 7 5 0 0 -6 -4 0 -6

Then, we multiply the elements of the diagonals going from the top left to the bottom right and add them together:

20-4 + -170 + 35-6 = -60

Next, we multiply the elements of the diagonals going from the bottom left to the top right and add them together:

003 + -672 + -45-1 = -84 + 20 = -64

Finally, we subtract the second sum from the first to get the determinant:

-60 - (-64) = 4

So, the determinant of the matrix is 4.