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 the form x=xh + p of Ax= (0, 6, -6)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
"the form x=xh + p of Ax= (0, 6, -6)T"
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