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Math Help - find this eigenvalue

  1. #1
    Junior Member
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    find this eigenvalue

    Find corresponding eigenvalue

    given: A= 2 -1 -1 x=1
    -1 2 -1 1
    -1 -1 2 1

    I figured that this matrix multiplied with that vector results in zero, hence eigenvalue can be zero, but I also figured that eigenvalue can be 3. Im now confused about possible eigenvalue. Help plz
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  2. #2
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    a matrix can (and usually does) have more than one eigenvalue.

    in this case, all you need to do is find the particular eigenvalue for a particular eigenvector, which you have done.
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  3. #3
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    If <1, 1, 1> is, in fact, an eigenvector for this matrix, then, by definition of "eigenvector", we must have
    [2 -1 -1][1] [1]
    [-1 2 -1][1]= L[1]
    [-1 -1 2][1] [1]

    Multiply the left side and see if it does give a multiple of <1, 1, 1> and what that multiple is.

    You did not need to calculate the possible eigenvalues in advance to do that.
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