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Eigenval/vect question, double check my answers, dont make sense

  1. Jul 11, 2011 #1
    eigenval/vect question, double check my answers, dont make sense.............

    1. The problem statement, all variables and given/known data
    find eigenvalues and eigenvectors of matrix A =
    102
    012
    223


    2. Relevant equations
    A -λI etc blah


    3. The attempt at a solution
    I'm getting λ = 1, -1, 5.

    For λ = 1, v = (-1,1,0)t (t being a real integer constant), and double checking says it's right.

    For λ = -1, i'm getting v = (1,1,1)t but if i double check by multiplying it with the matrix A i'm not getting something in the form of v (i'm getting like.. 3,3,7, which doesnt make sense to me).

    For λ = 5, i got v = (1,1,2)t but again double checking doesnt give a vector in this form! (multiplying this v by A gives me 3,3,14) :angry:

    what am i doing wrong??
     
  2. jcsd
  3. Jul 11, 2011 #2

    ehild

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    Re: eigenval/vect question, double check my answers, dont make sense.............

    (1,1,1) is wrong, it is (-1,-1,1).
    You do something wrong with matrix multiplication. How do you do it? The third eigenvector is correct.

    ehild
     
  4. Jul 11, 2011 #3
    Re: eigenval/vect question, double check my answers, dont make sense.............

    ok yeah my bad, the evect for lambda = -1 is (-1,-1,1) (i rushed).

    but multiplying A with (-1,-1,1) gives (-3,-3,7), which still doesnt make sense >:/
     
  5. Jul 11, 2011 #4

    lanedance

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    Re: eigenval/vect question, double check my answers, dont make sense.............

    i get (1,1,-1) as you would expect
     
  6. Jul 11, 2011 #5

    ehild

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    Re: eigenval/vect question, double check my answers, dont make sense.............

    How do you do the multiplication?

    Multiply (-1,-1,1) with the
    first column of the original matrix: -1+0+2=1;
    with the second column: 0-1+2=1;
    with the third column: -2-2+3=-1.
    The result is (1,1,-1) =-1(-1,-1,1) as it has to be.

    ehild
     
  7. Jul 11, 2011 #6
    Re: eigenval/vect question, double check my answers, dont make sense.............

    ok i was multiplying column of matrix by each row of the vector, when i should be multiplying the rows of the matrix by the vector and adding terms.

    my bad.
     
  8. Jul 11, 2011 #7

    ehild

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    Re: eigenval/vect question, double check my answers, dont make sense.............

    It is the same, you can multiply each element of a row of the matrix with the corresponding element of the vector, and ADD them - so is it OK now?

    ehild
     
  9. Jul 11, 2011 #8
    Re: eigenval/vect question, double check my answers, dont make sense.............

    A times (-1,-1,1) i (incorrectly) did:

    1x-1 + 0x-1 + 2x-1
    0x-1 + 1x-1 + 2x-1
    2x 1 + 2x 1 + 3x 1

    giving

    -1-2
    -1-2
    2+2+3

    resulting in (-3,-3,7)

    which is incorrect.

    i know how to do it now, thanks ehild and lanedance.
    shouldve remembered this from years ago...
     
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