After applying \(\mathbf M = \begin{pmatrix} -1 & 0 \\ -\sqrt 2 & 3 \end{pmatrix}\)to the circle of radius 3 centered at (2,0), what is the area of the resulting region?
Here's what I've done so far: I found two points - (2,0) and (-1,0), which I turned into vectors of \(\ \begin{pmatrix} 2\\ 0 \end{pmatrix}\)and \(\ \begin{pmatrix} -1\\ 0 \end{pmatrix}\) . I then multiplied these by the original matrix, to get \(\ \begin{pmatrix} -2\\ -2\sqrt2 \end{pmatrix}\) and \(\ \begin{pmatrix} 1\\ \sqrt2 \end{pmatrix}\) . I then calculated the distance between these two using the distance formula, which I got to equal \(\sqrt11\). I then plugged in \(\sqrt11\) to the circle area formula, ending up with a circle with area \(11\pi\). However, this answer is incorrect. Any tips on how I should solve this? Thanks!