
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 $\displaystyle x= x_b + x_p$, where $\displaystyle x_b$ is a solution of Ax = 0 and $\displaystyle x_p$ is a particular solution of Ax = b.
$\displaystyle
\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:
$\displaystyle
\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