## given system, find solns, show solns form vector space, and

Linear spaces and subspaces, linear transformations, bases, etc.
testing
Posts: 21
Joined: Sun Dec 07, 2008 12:26 am
Contact:

### given system, find solns, show solns form vector space, and

I need to find the set of solutions to a system of linear equations, show that they are a vector space of R^4, and find a basis for them. The equations are:

x1 - 2x3 - 3x4 = 0
x2 - 3x3 + x4 = 0
2x1 - x2 - x3 - 7x4 = 0

I got a solution of x = x3*(2, 3, 1, 0). I could show closure, but how do you find a basis with just the one vector?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: given system, find solns, show solns form vector space, and

I need to find the set of solutions to a system of linear equations, show that they are a vector space of R^4, and find a basis for them. The equations are:

x1 - 2x3 - 3x4 = 0
x2 - 3x3 + x4 = 0
2x1 - x2 - x3 - 7x4 = 0

I got a solution of x = x3*(2, 3, 1, 0). I could show closure, but how do you find a basis with just the one vector?
you should have two vectors that form your basis

(2,3,1,0) is correct

and the other is (3,-1,0,1)