Thread: Gauss-Jordan equation I am stuck on

I've never been any good at math, but I seem to be getting nowhere with this problem

4x + 4y + z - 6w = 0
-5x - y - 5z + 3w = 0
7x + 11y - 2z - 15w = 0


E-mailed the prof for help, told me this:

It is not a 'trick question', it is just one that you will have
infinitely many solutions (it cannot have just one, it does not have enough
equations, it cannot have no solution, because all the equations are set to
zero, so if all the variables are set to zero then the equations are
satisfied). It will have some almost nasty looking fractions in it (I
think). Don't let fractions scare you.

Any help is appreciated. Thanks so much.

Just row reduction my friend. Do the same thing you would do if there was unique solution, and express your answer in terms of free variables. Get as your answer {{x -> (3 w)/8 - (19 z)/16, y -> (9 w)/8 + (15 z)/16}}. Try it yourself and see!