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## Homework Statement

Find a basis for the solution space of the given homogeneous system.

x1 x2 x3 x4

1 2 -1 3 | 0

2 2 -1 6 | 0

1 0 0 3 | 0

## The Attempt at a Solution

When I reduced to reduced row echelon form i get the following matrix:

1 0 0 3 | 0

0 1 0 0 | 0

0 0 1 0 | 0

Which I thought it meant that the basis for the solution space would be:

1

0

0

-3

But apparently it isn't...what am I doing wrong?