Chapter 5.2, Problem 42E

The two column vectors ${\stackrel{\to }{v}}_1$ and ${\stackrel{\to }{v}}_2$ of a $2\times 2$ matrix Aare shown in the accompanying figure. Let $A=QR$ be the QR factorization of A. Represent the diagonal entries $r_{11}$ and $r_{22}$ of R as lengths in the figure. Interpretthe product $r_{11}$ $r_{22}$ as an area.