Chapter 3.1, Problem 43E

Let u = $\left[\begin{array}{c}\begin{array}{c}3\\ 0\end{array}\end{array}\right]$ and v = $\left[\begin{array}{c}\begin{array}{c}1\\ 2\end{array}\end{array}\right]$. Compute the area of the parallelogram determined by u, v, u + v, and 0, and compute the determinant of [u v]. How do they compare? Replace the first entry of v by an arbitrary number x, and repeat the problem. Draw a picture and explain what you find.