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Math Help - Eigenvectors and Eigenvalues

  1. #1
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    Eigenvectors and Eigenvalues

    It says: Show that v is an eigenvector of A and find the corresponding eigenvalue.



    A =
    [3 0 0
    0 1 -2
    1 0 1]



    v =
    [2
    -1
    1]
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  2. #2
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    Quote Originally Posted by nicolem1051 View Post
    It says: Show that v is an eigenvector of A and find the corresponding eigenvalue.



    A =
    [3 0 0
    0 1 -2
    1 0 1]



    v =
    [2
    -1
    1]
    v is an eigen vector iff Av=\lambda v where \lambda is the eigenvalue for v.

    Av=\begin{bmatrix}6 \\ -3 \\ 3 \end{bmatrix} =3v
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  3. #3
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    thank you so much, that's the answer I got but I don't understand why it is 3. For some reason I am not getting it
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  4. #4
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    to find the eigenvalues all u have to do is find the characteristic equation det(A-λI)=0

    for example..the matrix A[ 3 0 0
    0 1 -2
    1 0 1]

    u write it like this A[ 3-λ 0 0
    0 1-λ -2
    1 0 1-λ]
    and then you expand by Column 2
    and therefore u get (1-λ)(3-λ)(1-λ)=0
    hence the eigenvalues are λ=1, λ=3, λ=1.

    You can now find the corresponding eigenvectors u, v and w.
    Let u=[a,b,c]. If Au=λu where λ=1 and 3 in this case. u solve the system Au=λu and u find the eigenvectors.
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