Consider the system of equations

\[

\begin{aligned}

&x+y-z=a \\

&x-y+2 z=b .

\end{aligned}

\]

a) Find the general solution of the homogeneous equation.

b) A particular solution of the inhomogeneous equations when \(a=1\) and \(b=2\) is \(x=1, y=1, z=1\). Find the most general solution of the inhomogeneous equations.

c) Find some particular solution of the inhomogeneous equations when \(a=-1\) and \(b=-2\).

d) Find some particular solution of the inhomogeneous equations when \(a=3\) and \(b=6\).

[Remark: After you have done part a), it is possible immediately to write the solutions to the remaining parts.]