I have already found the eigen values for a particular linear transformation. Substituting with the eigenvalue $\lambda$ in a matrix I get:
$C=\begin{bmatrix}-1 & -1 & -2\\-1 & -1 & 2\\0 & 0 & 0 \end{bmatrix}\begin{bmatrix}x\\y\\t\end{bmatrix}=\begin{bmatrix}0\\0\\0\end{bmatrix}$
I have to find the fixed points and fixed lines. What does the last line being all $0$s tells us? Does that mean that the a fixed line is a line with the equation $l:x+y=0$ and that every point on that line is fixed?
Fixed point of $C$ would be a point z such that $Cz = z$ where $z = (x,y,t)$.
$$x+y+2t = x$$ $$x+y-2t = y$$
which implies $$x+y = 0$$ Therefore all points on the line $x+y = 0$ are fixed points and you can say that it is a fixed line.