nullspaces

It's said that the nullspace basis can be written as the pivot
variables be in terms of the free variables, when reducing them.

However, I have a problem. What happens when you have something like:

x1 = 0
x2 = 0
x3 = 0
x4 = 0

in a 4x4 matrix.

Also, what about

x1 = 0
x2 = 0
x3 = 0
0 = 0 (for x4)

Another one,
x1 = 0
x2 = 0
x3 = x4
0 = 0

As well as,
0 = 0
0 = 0
0 = 0
0 = 0

Any advice would be helpful.

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