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

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Posts: 2,144
Registered: 12/13/04
Linear algebra with slope.
Posted: Feb 11, 2013 5:38 AM
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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 ?

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