Let \(\mathbf{A} = \begin{pmatrix}1 & 1 \\ -2 & 1 \end{pmatrix} \)Then A maps a circle with center (1,1) and radius 2 pictured on the left below, to the output ellipse on the right:
What is the area of this ellipse?
The area of the ellipse is the area of the original circle multiplied by the determinant of matrix A.
I'll leave you to do the number crunching.
