## brinethery 3 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. brinethery

halp!

2. brinethery

@No-data

3. brinethery

no-dataaaa!

4. No-data

It really doesn't

5. No-data

??

6. brinethery

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

7. brinethery

@no-data see the pdf file.

8. No-data

ok

9. No-data

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

10. No-data

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

11. brinethery

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

12. No-data

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

13. No-data

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

14. No-data

I got 3 + 8t + 8 t^2

15. alexwee123

ugh linear algebra o.0

16. brinethery

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

17. brinethery

*the

18. No-data

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

19. No-data

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

20. brinethery

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

21. No-data

Ok

22. brinethery

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

23. brinethery

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

24. No-data

25. brinethery

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. brinethery

P2: ax^2 +bx +c

27. brinethery

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. No-data

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

29. No-data

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

30. No-data

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. No-data

take some rest if you need it.

32. No-data

are you allright?

33. brinethery

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

34. No-data

Ok.

35. brinethery

How are you?

36. No-data

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. No-data

with the results aligned in columns.

38. brinethery
39. No-data

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

40. No-data

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

41. No-data

it's blocked.

42. brinethery

That's okay

43. No-data

but what does it show the video?

44. brinethery

Argentine tango

45. brinethery

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

46. No-data

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

47. brinethery

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

48. No-data

look for punk tango on you tube.

49. No-data

that is the tango i want to dance haha

50. No-data

well thank you brinethery.

51. No-data

I really miss math.. snif snif haha

52. No-data

see you!

53. brinethery

bye