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

by memo_juentes
Tags: basis, linar algebra, math, spans
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memo_juentes
#1
Oct24-11, 09:05 PM
P: 8
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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vela
#2
Oct24-11, 10:34 PM
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You didn't reduce the matrix correctly. Fix that first.
memo_juentes
#3
Oct25-11, 10:26 AM
P: 8
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
#4
Oct25-11, 01:27 PM
Mentor
P: 21,397
Find a basis for the solution space of the given homogeneous system.

Quote Quote by memo_juentes View Post

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
#5
Oct25-11, 02:29 PM
P: 8
Ohh got it, seems pretty obvious now that i see it

Thanks a lot btw
Mark44
#6
Oct25-11, 04:10 PM
Mentor
P: 21,397
You're welcome!


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