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

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?

Related Calculus and Beyond Homework Help News on Phys.org
vela
Staff Emeritus
Homework Helper
You didn't reduce the matrix correctly. Fix that first.

I'm sorry I actually typed the matrix wrong when making this thread. The correct matrix is:

1 2 -1 3 |0
2 2 -1 6 |0
1 0 3 3 |0

Mark44
Mentor
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?
x1 = -3x4
x2 = 0
x3 = 0
x4 = x4

This means that any vector x in the solution space is a constant multiple of what vector?

Ohh got it, seems pretty obvious now that i see it

Thanks a lot btw

Mark44
Mentor
You're welcome!