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Homework Help: Matrix associated to eigenspaces

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a 2 x 2 matrix A for which:
    E2 = span (-3, 5)
    E1 = span (1, -2)
    where E is the eigenspace associated with each eigenvalue.

    2. Relevant equations

    3. The attempt at a solution

    I know that to find the eigenspace from the matrix A I would use the equation
    E2 = ker (2(Identity) - A) but I can't figure out how to go backwards from the eigenspaces to the matrix A.
  2. jcsd
  3. Nov 29, 2009 #2


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    Science Advisor
    Homework Helper

    All you need to define a 2x2 matrix is the value of A(v1) and A(v2) for any two linearly independent vectors v1 and v2. Can you start applying that to your problem?
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