Finding the basis for a subspace and relating it to the basis of the vector space

Question

Let's say we have a subspace $U$ defined by the set:

$U = span {((1, 2, 1, 2),(2, 1, 2, 1),(1, 1, 1, 0))}$,

which exists within a vector space $V$, where $V = \mathbb{R}^4$.

I've been asked to find the basis for $U$, which I found to be the set:

$((1,2,1,2),(0,1,0,0),(0,0,0,1))$, using row reduction of the matrix composed of the spanning set. But then the next part of the question asks me to 'complete the basis of $U$ to a basis of $V$'. I don't understand what the question means by 'completing'. Could anyone offer advice?

Answer 1

It means choosing a fourth vector so that your set spans $R^4$