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)

- anonymous

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- schrodinger

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- anonymous

halp!

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- anonymous

@No-data

- anonymous

no-dataaaa!

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## More answers

- anonymous

It really doesn't

- anonymous

??

- anonymous

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

- anonymous

@no-data see the pdf file.

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

I got 3 + 8t + 8 t^2

- alexwee123

ugh linear algebra o.0

- anonymous

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

- anonymous

*the

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Ok

- anonymous

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

- anonymous

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

- anonymous

what is your standard polynomial?

- anonymous

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

- anonymous

P2: ax^2 +bx +c

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

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.

- anonymous

take some rest if you need it.

- anonymous

are you allright?

- anonymous

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

- anonymous

Ok.

- anonymous

How are you?

- anonymous

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

- anonymous

with the results aligned in columns.

- anonymous

http://www.youtube.com/watch?v=Du84AF2VOWA&feature=related

- anonymous

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

- anonymous

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

- anonymous

it's blocked.

- anonymous

That's okay

- anonymous

but what does it show the video?

- anonymous

Argentine tango

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

look for punk tango on you tube.

- anonymous

that is the tango i want to dance haha

- anonymous

well thank you brinethery.

- anonymous

I really miss math.. snif snif haha

- anonymous

see you!

- anonymous

bye

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