Question

Suppose a, b, c and d are non-zero constants such that a d – b c = 1. Show that the augmented matrix a b | e
c d | f  always represents a consistent and independent system of linear equations, no matter what the values of e and f.

Answer 1

This is what I got so far and now I'm stuck:
\[\left[\begin{matrix}a & b | e \\ c & d|f\end{matrix}\right]\]
\[\left[\begin{matrix}ac & bc|ec \\ ac & ad|fa\end{matrix}\right]\]
\[\left[\begin{matrix}ac & bc|ec \\ 0 & ad-bc|fa-ec\end{matrix}\right]\]