Find a basis for the solution space of the given homogeneous system.by memo_juentes Tags: basis, linar algebra, math, spans 

#1
Oct2411, 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? 



#2
Oct2411, 10:34 PM

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,536

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




#3
Oct2511, 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 



#4
Oct2511, 01:27 PM

Mentor
P: 21,081

Find a basis for the solution space of the given homogeneous system.x_{1} = 3x_{4} x_{2} = 0 x_{3} = 0 x_{4} = x_{4} This means that any vector x in the solution space is a constant multiple of what vector? 



#5
Oct2511, 02:29 PM

P: 8

Ohh got it, seems pretty obvious now that i see it
Thanks a lot btw 



#6
Oct2511, 04:10 PM

Mentor
P: 21,081

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 