Register to reply

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

by memo_juentes
Tags: basis, linar algebra, math, spans
Share this thread:
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?
Phys.Org News Partner Science news on Phys.org
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home
vela
#2
Oct24-11, 10:34 PM
Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,670
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: 21,216
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: 21,216
You're welcome!


Register to reply

Related Discussions
Algebra, the basis of a solution space Calculus & Beyond Homework 2
A solution to a homogeneous system Calculus & Beyond Homework 2
Basis for the homogeneous system... Calculus & Beyond Homework 2
For what values of a does the following homogeneous system have a nontrivial solution Calculus & Beyond Homework 9
Solution space of linear homogeneous PDE forms a vector space?! Calculus & Beyond Homework 2