Date: Feb 12, 2013 5:17 AM
Author: mina_world
Subject: Re: Linear algebra with slope.

"JosÃ© Carlos Santos" ?? ??? ??? ??????.

ansb5mFmjobU1@mid.individual.net...

On 11-02-2013 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).

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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)