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

[memo_juentes]

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?

 

[vela]

You didn't reduce the matrix correctly. Fix that first.

 

[memo_juentes]

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]

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?

Your reduced matrix says this:
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?

 

[memo_juentes]

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

Thanks a lot btw

 

[Mark44]

You're welcome!