[mavroulis]

Um, I have these exercises for practising but I am really struggling doing them. I just need someone to help me with that so as to have some solutions in order to practise with and revise. Thank you in advance for your help.


Let Λ be a line in Real Projective Plane and its equation:
Ax + Bu + Ct = 0.
Let Λx, Λu, Λt be the lines in Real Projective Plane given by x = 0, u = 0, t = 0, respectively.

1)Find the intersections of Λx with Λu,Λx with Λt and Λt with Λu,

2)Find the intersection of Λ1 with Λ2 which is a subset of the Real Projective Plane, where Λ1 and Λ2 are lines in that, given by the equations x+u+t=0 and x-u=0 respectively.

3)Construct bijections Λx-> RP1 and Λu-> RP1 and Lt-> RP1 (Real Projective.. )

4) Put Ax = RP2 \ Λx, put Au = RP2 \ Λu, put At = RP2 \ Λt.
Show that :RP2 = Ax U Au U At (U is for union)