Reduce a set into linearly independent Consider the vectors in a set

$\text{span} \{<1, 4, 0, 2>, <3, 1, 4, 0>, <-1, 7, -4, 4>, <0, 11, -4, 6>\}$

the set is not linearly independent, what is a strategy into finding a useless vector and removing it from the span so the set becomes linearly independent? 

Let $A = \begin{pmatrix} 1 & 3 & -1 & 0 \\ 4 & 1 & 7 & 11 \\ 0 & 4 & -4 & -4 \\ 2 & 0 & 4 & 6 \end{pmatrix}_.$
If you row reduce $A$, you get the following matrix:
$$ \begin{pmatrix} 1 & 0 & 2 & 3 \\ 0 & 1 & -1 & -1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}_.$$
Picking out the vectors corresponding to the columns with leading ones, gives:
$$\begin{pmatrix} 1 \\ 4 \\ 0 \\ 2 \end{pmatrix} \text{ and } \begin{pmatrix} 3 \\ 1 \\ 4 \\ 0 \end{pmatrix}$$
These will be a basis for the span of the columns of $A$.
