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Let $A=\left(\begin{array}{rrr}1 & 1 & -1 \\ 1 & -1 & 2\end{array}\right)$

a) Find the general solution $\mathbf{Z}$ of the homogeneous equation $A \mathbf{Z}=0$.
b) Find some solution of $A \mathbf{X}=\left(\begin{array}{l}1 \\ 2\end{array}\right)$
c) Find the general solution of the equation in part b).
d) Find some solution of $A \mathbf{X}=\left(\begin{array}{l}-1 \\ -2\end{array}\right)$ and of $A \mathbf{X}=\left(\begin{array}{l}3 \\ 6\end{array}\right)$
e) Find some solution of $A \mathbf{X}=\left(\begin{array}{l}3 \\ 0\end{array}\right)$
f) Find some solution of $A \mathbf{X}=\left(\begin{array}{l}7 \\ 2\end{array}\right)$. [Note: $\left(\begin{array}{l}7 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 2\end{array}\right)+2\left(\begin{array}{l}3 \\ 0\end{array}\right)$ ].
[Remark: After you have done parts a), b) and e), it is possible immediately to write the solutions to the remaining parts.]
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