Finding Basis of Subspace

Procedure

1. Prove that the Subspace $S$ is a subspace with the Subspace Test
2. Sub in for the required amount of free variables to solve the equation, continue until you cannot find any more vectors that are linearly independent.

Alternate Procedure

1. For a given vector space $V$
2. Pick arbitrary $x\in V$, and express it as a combination of basic vectors
3. Create that set $S$ of those basic vectors