Results 1 to 3 of 3

Math Help - Change of basis

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    6

    Change of basis

    I have a question regarding change-of-basis matrices. In our literature, the following equation:
    (100a+100b,b) = a'(-1,2)+b'(1,2)
    yields as a result:
    a' = -(200a+199b)/4
    b' = (200a+201b)/4


    I do not understand how they get to this answer?
    I'm asking this because I would like to apply it to the following question:

    Consider two bases of R^2: B = {u1, u2} = {(1, -2), (3, -4)} and
    L = {v1, v2} = {(1, 3), (3, 8)}. Find the change-of-basis matrix P from B to L.

    From what I understand, you would have to find a,b,c,d so that:
    (1,-2) = a(1,3) + b(3,8) and (3,-4) = c(1,3) + d(3,8)

    But how do you go about this? I can see it with no calculations for easy answers, but for other matrices they are too complicated (like the one above where the answer would be-(200a+199b)/4). How do you get to such an answer?

    Thanks for the help you may give me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2011
    Posts
    6
    Uhm, sorry to have posted this question as my first post here. Because I have already figured it out myself. Sorry for the inconvenience.

    The answer should be to solve ((1,3),(3,8))|(1,-2) as a simple gauss elimination right? Ahh I feel so dumb, sorry again.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm glad you figured it out on your own. It would helpful if you were now to mark your thread as "Solved". Should be under the option "Thread Tools" near the top-right corner of the OP.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Change of Basis
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 2nd 2010, 06:16 AM
  2. Change of basis?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: March 12th 2010, 05:30 AM
  3. change of basis
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 19th 2009, 11:10 AM
  4. Change of Basis- Please help
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 18th 2009, 01:46 AM
  5. Change of Basis.
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 11th 2008, 05:14 AM

/mathhelpforum @mathhelpforum