# generating a vector given other vectors in modulo 11

how to show that vector $X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}$ can be generated with

$X1=\begin{bmatrix}9 & 1 & 0 & 0\end{bmatrix}$

$X2=\begin{bmatrix}8 & 0 & 1 & 0\end{bmatrix}$

$X3=\begin{bmatrix}7 & 0 & 0 & 1\end{bmatrix}$

in mod 11?

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$X4=\begin{bmatrix}0 \\ 2 \\ 1 \\ 1\end{bmatrix}=2\begin{bmatrix}9 \\ 1 \\ 0 \\ 0\end{bmatrix}+1\begin{bmatrix}8 \\ 0 \\ 1 \\ 0\end{bmatrix}+1\begin{bmatrix}7 \\ 0 \\ 0 \\ 1\end{bmatrix}$ $(\text{mod }11)$