Let $S$ be a region in the plane with area 4.  When we apply the matrix
\[\begin{pmatrix} 2 & -1 \\ 7 & 2 \end{pmatrix}\]to $S,$ we obtain the region $S'.$  Find the area of $S'.$
I know that the matrix transforms the plane by stretching, rotating, and possibly reflecting it. I also know that the determinant of the matrix tells me how much the area of any region is scaled by the transformation. So, to find the area of $S',$ I just need to multiply the area of $S$ by the absolute value of the determinant of the matrix. The determinant of the matrix is $2 \times 2 - (-1) \times 7 = 4 + 7 = 11.$ The absolute value of 11 is 11, so the area of $S'$ is $4 \times 11 = 44.$ 