> 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).