Question 5. (15 points) Let A be an 4 \times 4 matrix with columns $\vec{c_1}$, $\vec{c_2}$, $\vec{c_3}$, $\vec{c_4}$ (in that order) such that $\vec{c_1}$, $\vec{c_2}$, $\vec{c_3}$ are linearly independent and $\vec{c_4} = 2\vec{c_1} - \vec{c_2} + \vec{c_3}$. Find all solutions $\vec{x}$ to the linear system of equations $A\vec{x} = \vec{c_2}$ where $\vec{x} = \begin{bmatrix} x_1\\x_2\\x_3\\x_4 \end{bmatrix}$.