Express a vector as a combination of a linearly dependent set So I have to express the vector
\begin{pmatrix}
-2 \\
-4 \\
1 \\
0 \\
\end{pmatrix}
as a combination of these vectors:
\begin{pmatrix}
1 \\
0 \\
2 \\
1 \\
\end{pmatrix}
\begin{pmatrix}
1 \\
1 \\
0 \\
2 \\
\end{pmatrix}
\begin{pmatrix}
-1 \\
-3 \\
4 \\
-4 \\
\end{pmatrix}
\begin{pmatrix}
1 \\
2 \\
-1 \\
1 \\
\end{pmatrix}
But when I solved the augmented matrix, I got
\begin{pmatrix}
1 & 0 & 2 & 0 & -1 \\
0 & 1 & -3 & 0 & 2 \\
0 & 0 & 0 & 1 & -3 \\
0 & 0 & 0 & 0 & 0 \\
\end{pmatrix}
Meaning the system is linearly dependent. How should I go about expressing a linear combination without a linearly independent set?

I got the following set of equations:
$$\begin{align}
a_1 + 2a_3 &= -1 \\
a_2 - 3a_3 &= 2 \\
a4 &= -3
\end{align}$$
There were infinitely many solutions. I set $a_3 = 0$ and got the following as a valid linear combination:
$$-v_1 + 2v_2 + -3v_4$$
I tried this and got a failing answer before, but it was because I used $v_3$ in place of $v_4$.
