Chapter 2.2, Problem 25E

Exercises 25 and 26 prove Theorem 4 for A = $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$.

25. Show that if ad − bc = 0. then the equation Ax = 0 has more than one solution. Why does this imply that A is not invertible? [Hint: First, consider a = b = 0. Then, if a and b are not both zero, consider die vector x = $\left[\begin{array}{c}-b\\ a\end{array}\right]$.]