
Linear algebra with slope.
Posted:
Feb 11, 2013 5:38 AM


Hello teacher~
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). (Maybe, slope transformation of f.)
 Hm, is this possible problem? If possible, 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) It means that f(1,a) = (1,c).
is this right ?

