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

1. The problem statement, all variables and given/known data
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

3. 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?
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 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus 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

Mentor

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

 Quote by memo_juentes 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
 Mentor You're welcome!

 Tags basis, linar algebra, math, spans