## Matrix Consistency

Could you guys help me out with this problem:

(a) Determine whether the nonhomogeneous system Ax = b is consisent and (b) if the system is consistent, write the solution in the form $x= x_b + x_p$, where $x_b$ is a solution of Ax = 0 and $x_p$ is a particular solution of Ax = b.

$

\begin{pmatrix} 1 & -2 & 2 & 0 & 8\\0 & -6 & 2 & 4 & 5\\5 & 0 & 22 & 1 & 22\\3 & -8 & 4 & 0 & 19\end{pmatrix}

$

Which then resolves to:

$

\begin{pmatrix} 1 & -2 & 2 & 0 & 8\\0 & -6 & 2 & 4 & 5\\0 & 10 & 12 & 1 & -18\\0 & -2 & -2 & 0 & -5\end{pmatrix}

$

But now I'm stuck. Any help would be greatly appreciated.

Larson