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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.]
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