SOLUTION: Let A= [1 2 3 5;2 4 8 12;3 6 7 13] I have already reduced the matrix to [1 2 3 5;0 0 1 1;0 0 0 0] I need help solving the next step which is to find the general solution in t

 
Matrix A is an abbreviation for this system of equations:



You have reduced the matrix down to this, call it B:



That reduced matrix is an abbreviation for this system of equations:



Eliminating all the 0 terms and the 1 coefficients:



Substitute 1 for z in the first equation:








So the general solution is

x = 2-2y
y = y
z = 1

or

(x, y, z) = (2-2y, y, 1)

That's the way most books like the general solution in.

I've never seen 

though I've taught college mathematics for many years.  I'm sure
it's equivalent to that, though. Some books will put a k for the y,
like this:

(x, y, z) = (2-2k, k, 1)

Edwin