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Math Help - characheristic equation

  1. #1
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    Exclamation characheristic equation

    Please help me if you can.....big donation if it gets done
    1)find the eigenvalues for the matrix
    A = 1 2 1
    0 3 1
    0 5 -1
    B) for each eigenvalue found above find a basis for the eigenspace

    C)join all basis vectors from B) into a single set. does this set form a basis R^3? why or why not?

    D)use C to express the v= [4 2 8] as a linear combination of eigenvectors. then find A15 v without having to work too hard.

    2) repeat a-c for the matrix
    B= 1 5 1
    0 3 -1
    0 1 1
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Darren mcarty View Post
    Please help me if you can.....big donation if it gets done
    1)find the eigenvalues for the matrix
    A = 1 2 1
    0 3 1
    0 5 -1
    B) for each eigenvalue found above find a basis for the eigenspace

    C)join all basis vectors from B) into a single set. does this set form a basis R^3? why or why not?

    D)use C to express the v= [4 2 8] as a linear combination of eigenvectors. then find A15 v without having to work too hard.

    2) repeat a-c for the matrix
    B= 1 5 1
    0 3 -1
    0 1 1
    have you tried solving the characteristic polynomial |xI - A|? what was that?
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  3. #3
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    yes but i didnt know where to go after subtracting the lamda
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Darren mcarty View Post
    yes but i didnt know where to go after subtracting the lamda
    try factoring your char. poly.. ie, P_A (x) = (x-k_1)(x-k_2)...
    what was your char.poly and also the factored form?

    i got, P_A (x) = (x-1)(x-4)(x+2)
    so the eigenvalues are 1,4,-2..
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  5. #5
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    i did not get those ... but thanks at least i have something to work towards
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