Use the definition of Ax to write the matrix equation as a vector equation, or...

From the Theorem 3 the matrix equation is
${\displaystyle Ax=b}$
where A in ${\displaystyle m\times n}$ matrix ${\displaystyle b\in R^m}$.
We have
$x_1\left[\begin{array}{c}4\\ -1\\ 7\\ -4\end{array}\right]+x_2\left[\begin{array}{c}-5\\ 3\\ -5\\ 1\end{array}\right]+x_3\left[\begin{array}{c}7\\ -8\\ 0\\ 2\end{array}\right]=\left[\begin{array}{c}6\\ -8\\ 0\\ -7\end{array}\right]$
then the matrix equation of the given vector equation is
$\left[\begin{array}{c}{x}_1\cdot 4\\ -x_1\\ x_1\cdot 7\\ -x_1\end{array}\right]+\left[\begin{array}{c}-5x_2\\ 3\cdot x_2\\ -5x_2\\ x_2\end{array}\right]+\left[\begin{array}{c}7x_3\\ -8x_3\\ 0\\ 2\cdot x_3\end{array}\right]=\left[\begin{array}{c}6\\ -8\\ 0\\ -7\end{array}\right]$
$\left[\begin{array}{ccc}4& -5& 7\\ -1& 3& -8\\ 7& -5& 0\\ -4& 1& 2\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}6\\ -8\\ 0\\ 7\end{array}\right]$
Hence, the matrix equation is
$\left[\begin{array}{ccc}4& -5& 7\\ -1& 3& -8\\ 7& -5& 0\\ -4& 1& 2\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}6\\ -8\\ 0\\ 7\end{array}\right]$
Result: $\left[\begin{array}{ccc}4& -5& 7\\ -1& 3& -8\\ 7& -5& 0\\ -4& 1& 2\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]=\left[\begin{array}{c}6\\ -8\\ 0\\ 7\end{array}\right]$