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Formula for T with respect to Linear Transformations

  1. Jul 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Let T:P2 -> P2 be the linear operator by
    T(a0 +a1x + a2x = ao + a1 (x - 1) + a2 (x-1)2


    2. Relevant equations
    part a ask to find the matrix [T]B - did, see below
    part b ask to verify matrix [T]B satisfies every vector for [T]B [X]B = [T(X)]B?


    3. The attempt at a solution
    Matrix [T]B = 1 -1 1
    0 1 2
    0 0 1

    What is the given formula for T? I do not see this in the book to help solve this?
     
  2. jcsd
  3. Jul 8, 2009 #2

    Mark44

    Staff: Mentor

    I can't tell what you're trying to say here.


    Is the left side in your formula for your transformation T(a0 + a1x + a2x2)?

    Tip: Instead of typing in and , use the forum user interface to help you with this. Just below the input text box, there's a button labelled Go Advanced. After you click this button, there are a slew of buttons to help you format your work. The X2 can be used for exponents, and the X2 button can be used for subscripts. The exponents and subscripts can be anything, not just 2.
     
  4. Jul 8, 2009 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Ptricky! Welcome to PF! :smile:

    (and yes, do try using the X2 and X2 tags just above the Reply box :wink:)


    Write each element as a vector: (a0, a1, a2) …

    then what is T of (a0, a1, a2) ? :smile:
     
  5. Jul 8, 2009 #4
    Mark44

    Yes, that is the correct left side of equation.

    Don't mean to seam like an idiot but where again am I supposed to find this "go advanced" tab? Just below the "input text box" my choices are "submit reply" and "preview post". Below that is "additional Options", I do not see "go Advanced" - sorry!

    I have all the little icons right of "fonts and sizes" but none are "go advanced"?
     
  6. Jul 8, 2009 #5
    Re: Welcome to PF!

    Tiny-Tim,

    Thanks for the welcome! My tags are up, I see the difference in options from the quick reply options!

    I did 'click' the tags for super and sub. The notation shown is what I get and . Any explanation?
     
  7. Jul 8, 2009 #6

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Ptricky! :smile:
    erm :redface:

    you have to put something inside the tag! :biggrin:
    (eg P2 P2 :wink:)
     
  8. Jul 8, 2009 #7
    Tiny-Tim,

    figured out the formula input notation! I will retype my question.
     
  9. Jul 10, 2009 #8
    Does

    T(x) = ao + a1x -a1
    ;a2 x - 2a2 + a2

    if so how do I prove this for every x = a0 + a1x + a2x2 in P2?
     
  10. Jul 10, 2009 #9

    tiny-tim

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    Science Advisor
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    Hi Ptricky! :wink:
    No … try again!

    And when you've got it right, put it in the form b0 + b1x + b2x2 :smile:
     
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