Chapter 1.3, Problem 18E

Let A be a $2\times 2$ matrix with $a_{11}\ne 0$ and let $\alpha =a_{21}/a_{11}$ . Show that A can be factored into a product of the form

$\left[\begin{array}{cc}1& 0\\ \alpha & 1\end{array}\right]\left[\begin{array}{cc}{a}_{11}& a_{12}\\ 0& b\end{array}\right]$

What is the value of b?