Let the system of linear equations

x + y + $\alpha$z = 2

3x + y + z = 4

x + 2z = 1

have a unique solution (x$^ * $, y$^ * $, z$^ * $). If ($\alpha$, x$^ * $), (y$^ * $, $\alpha$) and (x$^ * $, $-$y$^ * $) are collinear points, then the sum of absolute values of all possible values of $\alpha$ is