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Find 2 linearly independent eigenvectors and a eigenvalue

  1. Oct 8, 2008 #1

    I am supposed to, without calculation, find 2 linearly independent eigenvectors and a eigenvalue of the following matrix A

    5 5 5
    5 5 5
    5 5 5

    The eigenvalue is easy -- it is 15. And I can find one eigenvector, [1 1 1] (written vertically), but another without calculation? Is there a trick that I should see? Of course, zero is also a eigenvalue, but how am I supposed to find the other eigenvector without calculation? Is there something that I should see?

  2. jcsd
  3. Oct 8, 2008 #2


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    Science Advisor
    Homework Helper

    Re: eigenvalues/vectors

    Pick the vector (x,y,z) so that 5x+5y+5z=0. Say, (1,1,-2)?
  4. Oct 8, 2008 #3
    Re: eigenvalues/vectors

    oh thanks!
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