1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A linear algebra problem.

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data
    A is a 2x2 matrix with eigenvectors 1,-1 and 1,1 with respective eigenvalues 2 and 3. x is 2,0. Find (A^4)x

    2. Relevant equations
    I know (A^k)v=(lamda^k)v
    But I just don't know how to solve this to find A and then multiple it by x

    3. The attempt at a solution
    See above

    Thanks a lot for anyone's help or input!
  2. jcsd
  3. Nov 25, 2008 #2


    User Avatar

    The eigenspace is two dimensional since there are two distince eigenvalues. Thus, A is diagonalizable. Then....
  4. Nov 25, 2008 #3


    User Avatar
    Science Advisor

    More simply, <2, 0>= <1, -1>+ <1, 1>. Apply A to that. You don't need to determine A itself.
  5. Nov 25, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    You don't need to find A. (2,0)=(1,-1)+(1,1). How would you find A^4((1,-1))?
  6. Nov 25, 2008 #5
    Ah I got it, (A^k)x=(lamda1^4)v1+(lamda2^4)v2

    Thanks a lot for pointing out that those two vectors added up to x, I overlooked that. Would this be possible otherwise?
  7. Nov 25, 2008 #6


    User Avatar
    Science Advisor
    Homework Helper

    If the only information you have about A is it's eigenvectors, and you can't express the vector as a linear combination of eigenvectors, then, no, you don't have enough information about A.
  8. Nov 25, 2008 #7
    Thank you very much you guys are awesome.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook