
Re: Linear algebra with slope.
Posted:
Feb 12, 2013 5:17 AM


"José Carlos Santos" ?? ??? ??? ??????. ansb5mFmjobU1@mid.individual.net...
On 11022013 10:38, mina_world wrote:
> Linear transformation f : R^2 > R^2. > Let M be the standard matrix of f. > Let Rank(M) = 1 or 2. > > Given a straight line y = ax+b. > > Then f transforms this line(y=ax+b) into > a line(y=cx+d) OR a fixed point. > > If y=cx+d line exists, show that (1,c) = f(1,a).
This can't be true. If f(x,y) = (2x,2y), then _f_ has rank 2 and transforms the line y = x into itself. But f(1,1) = (2,2).
 Oh, yes. you're right. In fact, my interest is slope. If I revise original post, "If y=cx+d line exists, show that c/1 = v/u when f(1,a)=(u,v)."
If, in this case, pf) y = ax+b ==> (x,y) = (1, a)*t + (0,b) (verctor) so, f(x,y) = f{(1,a)*t} + f(0,b) so, f(x,y) = t*f(1, a) + f(0,b) ==> this line y=cx+d It means that c/1 = v/u when f(1,a)=(u, v)

