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Transition and coordinate matrices

  1. May 2, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider the bases B = {b1,b2} and B' = {b'1,b'2} for R2, where

    b1=(1, -1), b2=(2,0), and b'1=(1,2), b'2=(1,-3)

    a. Find the transition matrix P from B to B'
    b. Compute the coordinate matrix [p]B, where p=(4,3); then use the transition matrix P to compute [p]B'

    2. Relevant equations


    3. The attempt at a solution
    a. I found the transition matrix P to be
    2/5 6/5
    3/5 4/5

    b. I found [p]B to be (-3, 7/2)
    and then I found [p]B' to be (3,1)

    Does this look correct? I am tripping out because this seems like something we covered in class months ago but this problem was just assigned this week. Am I missing something? Would the problem be different if B' represented an orthogonal basis? Any help is appreciated :)
     
  2. jcsd
  3. May 2, 2015 #2

    PeroK

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    Science Advisor
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    You should be able to check your answers for yourself on this one. For example, to check the vectors are correct you simply check that:

    ##-3b_1 + (7/2)b_2 = -3(1, -1) + 7/2(2, 0) = (-3, 3) + (7, 0) = (4,3)##

    So, (4, 3) is indeed (3, 7/2) in basis B.

    Etc.

    And, you can use the transition matrix to operate on the vectors to check that it does map the vectors correctly. This is often a good thing to check in any case.

    Everything looks correct, but I'd suggest you check them yourself.
     
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