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Calculate the eigenvectors of a specific matrix

  1. Apr 27, 2014 #1
    Hello,
    I'm really having a problem to calculate the eigenvectors of a specific matrix, i'm used to do this but i don't know why I'm stuck at this one
    1. The problem statement, all variables and given/known data

    A=
    2 1 0 1
    0 3 -1 0
    0 1 1 0
    0 -1 0 3

    λ1=2 multiplicity 3
    λ2=3 multiplicity 1

    A-2I=
    0 1 0 1
    0 1 -1 0
    0 1 -1 0
    0 -1 0 1

    The eigenvectors are given
    [-1 -1 -1 -1]
    [0 1 2 0]
    [1 0 0 0]

    If I solve
    (A-2I)xi=0
    I have
    x1=0
    x2+x4=0
    x2-x3=0
    -x2+x4=0


    I have to use this for differential equations, and my linear algebra course is far behind, I don't remember what I'm supposed to do when we get the first eigenvector =0, because when the multiplicity of the eigenvalue is > 0 we use the first one to find the following eigenvectors

    Thanks!
     
  2. jcsd
  3. Apr 27, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There is a nonzero eigenvector corresponding to eigenvalue 2. Rethink your conclusion that solving that matrix gives you x1=0.
     
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