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Linear Transformations and Coordinate

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Let B be a basis of R^2 consisting of the vectors <5,2> and <1,5> and let R be the basis consisting of <2,3> and <1,2>

    Find a matrix P such that [x]_r=P[x]_b for all x in R^2
    2. Relevant equations

    Ax=B?

    3. The attempt at a solution


    I attempted by using Ax=B as a format to solve for P, or x in the equation. I took the inverse of the column matrix of B because B is a basis, and if I am correct, a matrix's basis is defined as its coordinates ([x]_b).

    I understand the geometrical interpretation of a linear transformation, yet I have no idea how to represent the transformation as a matrix. I would love an in depth description to approach similar exercises.
     
    Last edited: Mar 27, 2010
  2. jcsd
  3. Mar 27, 2010 #2

    gabbagabbahey

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    Not quite. The relevant equation in this case is the one given in the problem statement.

    [tex][x]_r=P[x]_b[/tex]


    How would you go about represented a general vector [itex]x[/itex] in the B-basis?
     
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