brinethery
Find the matrix of the linear transformation T(f(t)) = f(2t+1) from P2 to P2 with respect to the basis B (script B) = (f1 = 1 +2t^2, f2=1, f3=t)



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brinethery
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halp!

brinethery
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@Nodata

brinethery
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nodataaaa!

Nodata
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It really doesn't

Nodata
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??

brinethery
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Fallingangel, don't ever take linear algebra. It is the worstest!

brinethery
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@nodata see the pdf file.

Nodata
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ok

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I think you need to apply the transformation to each vector of the basis.

Nodata
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and you form a matrix with the coefficients of the result in columns.

brinethery
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So would the first vector in the basis for f1 be [1,0,2] because of the standard basis [1,x,x^2]?

Nodata
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I thought that is the way, but I'm checking. if its true.

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Hmm what is the result of apply the transformation to the f_1 vector?

Nodata
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I got 3 + 8t + 8 t^2

alexwee123
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ugh linear algebra o.0

brinethery
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haha true alex. It's sht sh(((ts

brinethery
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*the

Nodata
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\[T(f_1(t)) = f_1(2t+1)=1+2(2t+1)^2\]

Nodata
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I got \(3 + 8t + 8t^2\) am I right?

brinethery
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sec... I think there's something more you have to do. Let me pull up some pages from a book.

Nodata
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Ok

brinethery
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So it looks like you first have to plug 2t+1 into the x's in your standard P2 polynomial first.

brinethery
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So you'll have 4t^2+4t+1

Nodata
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what is your standard polynomial?

brinethery
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I guess I meant plug in 1 +2t^2 into our polynomial.
4(1+2t^2)^2 +4t +1 = 4(1+2t^2)(1+2t^2) +4t +1
=4(1 + 4t^2 +4t^4) +4t +1

brinethery
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P2: ax^2 +bx +c

brinethery
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See I'm really confused. I think I'm going to stop right there b/c I'm not on the right track I don't think.

Nodata
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You need to remember how to obtain the matrix of a transformation first.

Nodata
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Always go back to your definitions and well understood theorems brinethery.

Nodata
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Right now I don't remember well, and I don't have math books at work to help you as I wish. But I think that is the way.

Nodata
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take some rest if you need it.

Nodata
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are you allright?

brinethery
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I'm fine, I just really need help to this question

Nodata
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Ok.

brinethery
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How are you?

Nodata
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As I said you before, you just need to apply the transformation to each of the vectors of your basis. and form a matrix.

Nodata
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with the results aligned in columns.


Nodata
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I mean: \[\left[\begin{matrix} F^T(f_1(t))& F^T(f_2(t)) & F^T(f_3(t)) &\end{matrix}\right]\]

Nodata
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Sorry I can't see you tube videos at work. =(

Nodata
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it's blocked.

brinethery
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That's okay

Nodata
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but what does it show the video?

brinethery
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Argentine tango

brinethery
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My goal in life is to travel to Buenos Aires and learn tango there

Nodata
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You mean one of the many goals on your life =P

brinethery
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I have no other goals. If I could just dance then I would be happy lol

Nodata
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look for punk tango on you tube.

Nodata
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that is the tango i want to dance haha

Nodata
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well thank you brinethery.

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I really miss math.. snif snif haha

Nodata
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see you!

brinethery
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bye