So I have the following set of linear equations:

x + 2y - z = 1

-x -2y + 3z = 0

x + y + z = -2

I then used Gaussian Elimination to simplify them, from which I obtained the Matrix:

6 0 0 -15

0 -12 0 -16

0 0 6 -5

first of all, my calculations could well be wrong, but I think i did it right. More to the point, I am more struggling with how to interpret the results. So from this matrix, do I take from it that, the system has a unique solution? the system has no solution? or the system has an infinite number of solutions?

Obviously the answer will also rely on whether or not my Gaussian Elimination is correct!

Thanks