What are the homogeneous coordinates $\lambda, \mu$ of the line $r: x_0+x_1=0$ in the projective frame $[0,0,1], [1,-1,0], [1,-1,2]$ in the projective plane $\Bbb P^2(\Bbb R)$ with associated homogeneous coordinates $x_0, x_1, x_2$? Aren't they $\lambda =0, \mu =1$? (and why?)
EDIT:
The rest of the exercise is:
$r': x_0-x_2=0$ is another line in $\Bbb{P^2(R^)}$ and $\lambda',\mu'$ are its coordinates in the projective frame $[0,1,0],[1,0,1],[2,3,2]$ (fundamental and unity points). Let $P_0[1,0,0] \not\in r\cup r'$ and $f: r\rightarrow r'$ such that $f(P)=L(P,P_0)\cap r'$.
I have to write the expression of $f$ in the coordinates $[\lambda,\mu]$, $[\lambda',\mu']$ and see that $f$ is an isomorphism.