Re: nullspaces

In article <1159364736.591184.155220@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, boo
<da.perk@xxxxxxxxx> wrote:

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:

I hope you mean what I think you mean>

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

in a 4x4 matrix.

Only (0, 0, 0, 0) is a solution - the coefficient matrix is
non-singular.

Also, what about

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

(0, 0, 0, x) is a solution for every x.

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

(0, 0, x, x) is a solution for every x.

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

(u, v, x, y) is a solution for every u, v, x and y - a rare occasion.

--
Paul Sperry
Columbia, SC (USA)
.