Finding the linear combination of a vector that is in a span So say we have
Span S =
$
        \begin{Bmatrix}
        \begin{bmatrix}
        1 \\
        0 \\
        1 \\
        \end{bmatrix}
        \begin{bmatrix}
        -1 \\
        1 \\
        1 \\
        \end{bmatrix}
        \begin{bmatrix}
        1 \\
        1 \\
        3 \\
        \end{bmatrix}
        \end{Bmatrix}
$
I know that 
$
        \begin{bmatrix}
        -1 \\
        4 \\
        7 \\
        \end{bmatrix}
$
is in the span because the reduced row echelon form of [A v] is consistent. Now 
how do I find what exactly the linear combination that makes the vector?

$$\begin{pmatrix}-1\\4\\7\end{pmatrix}=3\begin{pmatrix}1\\0\\1\end{pmatrix}+4\begin{pmatrix}-1\\1\\1\end{pmatrix}.$$
$$\begin{pmatrix}-1\\4\\7\end{pmatrix}=-5\begin{pmatrix}1\\0\\1\end{pmatrix}+4\begin{pmatrix}1\\1\\3\end{pmatrix}.$$
