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Math Help - eigenvectors

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    45

    eigenvectors

    Hi all,

    For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

    First i found the eigenvalues by letting det(A- lamba*I) = 0....
    the eigenvalue is lamda = 1

    I then solve for my eigenvector

    (A - I)v = 0

    i row reduce (A - I) to [0 2; 0 0]

    Now i am stuck... i don't know how to get my eigenvector

    Thanks in advance,
    ArTiCk
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  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi there

    Quote Originally Posted by ArTiCK View Post
    Hi all,

    For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

    First i found the eigenvalues by letting det(A- lamba*I) = 0....
    the eigenvalue is lamda = 1

    I then solve for my eigenvector

    (A - I)v = 0

    i row reduce (A - I) to [0 2; 0 0]
    \begin{pmatrix} 0 & 2 \\ 0 & 0 \end{pmatrix}

    means, that you have to solve 2 equations

    0*x+2*y = 0

    0*x+2*y = 0

    => y = 0 and any x

    x=1, x= 3 , x= - 10....

    \begin{pmatrix} x \\ 0 \end{pmatrix} is eigenvector
    and they are linearly dependent,....
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