Check out this thread. You'll have to scroll down past the first few posts if you want a rigorous proof (my first idea was incorrect).
I think that thread was a bit beyond the scope of my ability at this point. So I will probably have to bite the bullet on this problem. I am not sure how to find a determinant when there are variables in the solution vector. Do I simply find the determinant of the matrix on the left and find where it is zero?
It is a real mystery why some profs give questions like these with no explanation. ;< ;<