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Topic: Linear algebra with slope.
Replies: 2   Last Post: Feb 12, 2013 5:17 AM

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Jose Carlos Santos

Posts: 4,872
Registered: 12/4/04
Re: Linear algebra with slope.
Posted: Feb 11, 2013 8:48 AM
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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).

Best regards,

Jose Carlos Santos



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