I need help to find the vector parametric form of the following linear system.
I have tried doing it on my own but I can't seem to get the system in the right form to get a solution.
\begin{align*}
\begin{cases}
x - 2y - z = -4\\\\
-2x + 4y + 3z = 1
\end{cases}
\end{align*}
If we add twice the first row to the second row, we get that $z = -7$, as you have mentioned.
Based on it, we obtain the relation $x - 2y + 7 = -4$. That is to say, $x = 2y - 11$.
Consequently, the solution set to this system of linear equations is given by \begin{align*} S = \{(2a - 11,a,-7)\in\mathbb{R}^{3} \mid a\in\mathbb{R}\} \end{align*}
Hopefully this helps!