I have the following problem in my homework
Suppose a, b, are two constant paramaters such that the system below is consistent for any values of f and g. What can you say about the numbers a and b? Justify your answers.
x1+ax2 = f
bx1+ x2 = g
Am I under thinking this? Wouldn't a or b just have to be real numbers?
To always be consistent, $\begin{bmatrix}1&a\\ b&1\end{bmatrix}$ must be invertible, i.e. nonzero determinant, so any real numbers $a,b$ with
$1-ab\neq 0$