Answer
u$\begin{bmatrix} -2 \\ 1 \\0\end{bmatrix}$ + $\begin{bmatrix} -3 \\ 0 \\2 \end{bmatrix}$; no solution
Work Step by Step
We know that x = $ x_{p}$ + $x_{n}$
In the first part, subtracting two times first row from second row gives
$\begin{bmatrix} 1 & 2 & 2 \\ 0 & 0 & 1 \end{bmatrix}$ = $\begin{bmatrix} 0 \\ 0\end{bmatrix}$;
which gives $x_{n}$ =u $\begin{bmatrix} -2 \\ 1 \\0\end{bmatrix}$
setting the free variable 'v' in the original two equations as 0 gives $x_{p}$ as $\begin{bmatrix} -3 \\ 0 \\2 \end{bmatrix}$.
In second part, no solutions exist as row 2 is 2 times row 1, but 4 is not 2 times 1. Hence,geometrically this represents two parallel lines.
