My question is how to find the dimension of something.
Let's say: x1-2x2+x3-x4=0
and let's do one with more than 1 equation.
The Attempt at a Solution
For the second one I figured that if I took the basis of it, then however many vectors were in the basis would be equivalant to the dimensions.
So the transpose is
then I row reduced, and took the transpose and got
1 0 0 0
0 1 0 0
This is the basis, so I would say the dimension is 2, because that is the number of column vectors.
For the first one if you go over the same process you will get one vector, and I would assume that means the dimension is 1, but dimension is actually three and I have no idea how.
What should I do different for the first one?