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Linear Transformation from R^2 to R^3 
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#1
Dec2908, 10:06 AM

P: 726

Suppose a linear transformation [tex] T: R^2 \rightarrow R^3 [/tex] was defined by [tex] T(a_1,a_2) = (2a_1, a_2 + a_1, 2a_2)[/tex]. Now, for example, would I be allowed to evaluate [tex]T(3,8,0)[/tex] by rewriting (3,8,0) as (3,8)?



#2
Dec2908, 10:22 AM

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P: 2,616

In your case, how ever, it is not clear cut as to why we should interpret (3,8,0) as (3,8). Why couldn't it be seen as (8,0) instead? 


#3
Dec2908, 10:42 AM

P: 726

It seems to me that (3,8,0) and (3,8) represent the same location, if you interpret the coordinates geometrically. My highschool math teacher said that this practice was allowed when evaluating cross products, so I thought it might have been okay here. For example, the cross product isn't defined in R^2. So if you wanted to find the cross product of (3,4) and (4,6), you would simply rewrite it as (3,4,0) and (4,6,0).



#4
Dec2908, 11:09 AM

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P: 2,616

Linear Transformation from R^2 to R^3
Well it depends on the context. If you're an engineering student of course it makes sense to do so. But from a mathematical perspective it's not. It's only ok if it's understood to be intentionally omitted.
By the way you posted this in the Linear Algebra forums. Posting it elsewhere might net you a different answer. Don't try it though, since duplicate threads across different forums are frowned upon. 


#5
Dec2908, 03:04 PM

P: 726

Thanks for the help (I was only concerned with the mathematical viewpoint).



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