## anonymous 4 years ago 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)

1. anonymous

halp!

2. anonymous

@No-data

3. anonymous

no-dataaaa!

4. anonymous

It really doesn't

5. anonymous

??

6. anonymous

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

7. anonymous

@no-data see the pdf file.

8. anonymous

ok

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

I got 3 + 8t + 8 t^2

15. alexwee123

ugh linear algebra o.0

16. anonymous

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

17. anonymous

*the

18. anonymous

$T(f_1(t)) = f_1(2t+1)=1+2(2t+1)^2$

19. anonymous

I got $$3 + 8t + 8t^2$$ am I right?

20. anonymous

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

21. anonymous

Ok

22. anonymous

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

23. anonymous

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

24. anonymous

25. 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

26. anonymous

P2: ax^2 +bx +c

27. 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.

28. anonymous

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

29. anonymous

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

30. 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.

31. anonymous

take some rest if you need it.

32. anonymous

are you allright?

33. anonymous

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

34. anonymous

Ok.

35. anonymous

How are you?

36. 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.

37. anonymous

with the results aligned in columns.

38. anonymous
39. anonymous

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

40. anonymous

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

41. anonymous

it's blocked.

42. anonymous

That's okay

43. anonymous

but what does it show the video?

44. anonymous

Argentine tango

45. anonymous

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

46. anonymous

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

47. anonymous

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

48. anonymous

look for punk tango on you tube.

49. anonymous

that is the tango i want to dance haha

50. anonymous

well thank you brinethery.

51. anonymous

I really miss math.. snif snif haha

52. anonymous

see you!

53. anonymous

bye