Linear Algebra: solve system; show soln space as vector span

I'm taking Differential Equations and Linear Algebra (a combination class), but my question has to do with linear algebra. So I think this is the right place for my question. The question states the following:

Solve the system
First line: [1 3 1][x1]=[0]
second line: [0 8 9][x2]=[0]
third line: [0 4 4][x3]=[0]

Show your solution space as the span of some vectors.

(Sorry; I don't know the correct way to write matrices.)

I got it in reduced form:

First line: [1 3 1]
Second line: [0 8 9]
Third line: [0 0 1]

Wouldn't it be linearly independent, because x3 = x2 = x1 = 0? Wouldn't that be the answer? Can anyone help? Thanks!!!

To solve that system you should set up a matrix.


1 0 0 | 0

3 8 4 | 0

1 9 4 | 0

Then reduce the matrix to RREF (reduced row echelon form) If you can do that, you'll either have your answer or there will be no solution.

Does that help?

the problem is set up like this
1 3 1 l 0
0 8 9 l 0
0 4 4 l 0
I reduced it to
1 3 1 l
0 8 9 l
0 0 1 l
wouldn't that be linearly independent? my prof said it doesn't have to be in reduced echelon form you can just reduce it if you want.