Problem 4 (10 points):
(a) Find the 4 \times 4 matrix $A$ such that
$\begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{pmatrix} = \begin{pmatrix} x_1 - 2x_3 + x_4 \\ 3x_2 - x_3 \\ x_1 + x_2 - x_4 \\ x_3 - x_4 \end{pmatrix}$
for all $x_1, x_2, x_3, x_4 \in \mathbb{R}$.
(b) Find the 4 \times 4 matrix $A$ that swaps the first and fourth row, adds three copies of the first
row and one copy of the third row to the second row, and subtracts the fourth row from
the third row.
