Answer
x = -2a
y = -a
z = a
w = a
Where a is any real number
Work Step by Step
The reduced row-echelon form of the matrix is:
$\begin{bmatrix}
1 & 0 & 0 & 2 & |0\\
0 & 1 & 0 & 1 & |0\\
0 & 0 & 1 & -1 & |0\\
\end{bmatrix}$
We can write the solution as:
x + 2w = 0
y + w = 0
z - w = 0
We then can write the system in terms of w:
x = -2w
y = -w
z = w
To not use one of the variables in the system we can use a:
x = -2a
y = -a
z = a
w = a
Where a is any real number
