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How can be demostrated that affine transformations transform lines in lines?

i have just began studying functions, and i read in the chapter about geometric trnsformations that an \'affine transformation\': x\'= ax+by+c y\'= cx+dy+e 1) always transforms lines into lines, and i managed to demonstrate it mathematically 2) each transformation that implies a transformation of lines into lines must be an \"affine\" an described before.....well, i found demonstrating this very difficult...can anybody help me?? thanks to everyone!
Question asked by: dariogar

Asked on: 11 Feb 2010

That does sound difficult!

I have never heard of affine ones.

Hopefully someone else will be able to help you with your enquiry.

By: knowitall
Replied at: 21 Feb 2010
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Im not sure what you are saying is totally correct. Affine transforms send a variable x to a linear map in another vector space. As to showing the other way I would suggest possibly my matrix multiplication if you know how to do this
By: IsaacN

Date of comment: Tue, Jun 8th 2010

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Question Keywords

lines  transformations  transform  affine  demostrated  

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