3 Let $\beta$ be any number and consider the system of equations:
$x - \beta y = 1$
$\beta x - y = -1$
For which values of $\beta$ is the system (i) inconsistent (ii) consistent with a unique
solution (iii) consistent with infinitely many solutions?
[Hint: row reduce the matrix as normal, but be careful if you come to a point
where you might be dividing by zero. For example, if you wanted to divide a
row by $k$, you need to divide into two cases: (i) $k \neq 0$ when you can divide
through by $k$ and continue, and (ii) $k = 0$ when you can replace all $ks$ by zero
and continue.]
