Let $p_1 = 1 - 2t - t^2$, $p_2 = t + t^2 + t^3$, $p_3 = 1 - t + t ^3$ and $p_4 = 3 + 4t + t^2 + 4t^3$.
Let $S$ be the set of these four functions. Find a subset of $S$ that is a basis for the span of $S$.
So I've started out by taking these functions, making them vectors and putting them into a matrix:
$ \begin{bmatrix} 0 & -1 & -2 & 1\\ 1 & 1 & 1 & 0\\ 1 & 0 & -1 & 1\\ 4 & 1 & 4 & 3 \end{bmatrix} $
Then I reduced it:
$ \sim \begin{bmatrix} 1 & 0 & 0 & 1\\ 0 & 1 & 0 & -1\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix} $
I guess my question is, is this the correct way to do this? Where do I go from here? What does a zero row mean for a basis?