Find a basis for the subset

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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?
 

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