How Do You Determine a Basis for a Set of Vectors?

[nicnicman]

Homework Statement

Find a basis for the subset S = {(1, 2, 1), (2, 1, 3), (1, -4, 3)}

Homework Equations

The Attempt at a Solution

I'm not absolutely sure I'm doing this correctly but here is my attempt:

First, I put the vectors in S in the rows of a matrix (using multiple square brackets rather than one set of larger ones):
[1 2 1]
[2 1 3]
[1 -4 3]
Then, I found the row-reduced echelon form:
[1 0 5/3]
[0 1 -1/3]
[0 0 0]
So, a basis for the subset would be {(1, 0, 5/3), (0, 1, -1/3)}.

Is this correct?

 

[The Electrician]

Have a look at this page:

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=bas