Chapter 3.1, Problem 42E

Let u = $\left[\begin{array}{c}\begin{array}{c}\text{a}\\ \text{b}\end{array}\end{array}\right]$ and v = $\left[\begin{array}{c}\begin{array}{c}\text{c}\\ \text{0}\end{array}\end{array}\right]$, where a, b, and c are positive (for simplicity). Compute the area of the parallelogram determined by u, v, u + v, and 0, and compute the determinants of the matrices [u v] and [v u]. Draw a picture and explain what you find.