Answer
x = 0
y = -4a + 2
z = a
Where a is any real number
Work Step by Step
The reduced row-echelon form of the matrix is:
$\begin{bmatrix}
1 & 0 & 0 & |0\\
0 & 1 & 4 & |2\\
0 & 0 & 0 & |0\\
0 & 0 & 0 & |0\\
\end{bmatrix}$
We can write the solution as:
x = 0
y + 4z = 2
We then can write the system in terms of z:
x = 0
y = -4z + 2
To not use one of the basis variables we can use a:
x = 0
y = -4a + 2
z = a
Where a is any real number
