Consider the matrix \(\mathbf{A} = \begin{pmatrix} 1 & 1 \\ 2 & 1 \end{pmatrix}\)
and the parallelogram in the picture below:
Say that A maps \(P_1\) to \(Q_1\) , \(P_2\) to \(Q_2\), \(P_3\) to \(Q_3\) , and \(P_4\) to \(Q_4\). Then what is the ordered pair \((\text{Area of } P_1P_2P_3P_4, \text{Area of } Q_1Q_2Q_3Q_4)?\)
