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Math Help - finding eigenvectors

  1. #1
    Member Jskid's Avatar
    Joined
    Jul 2010
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    160

    finding eigenvectors

    Find the characteristic polynomial, eigenvalues and eigenvectors of the matrix <br />
\[<br />
A =<br />
\begin{array}{ccc}<br />
0 & 1 & 2 \\<br />
0 & 0 & 3 \\<br />
0 & 0 & 0 \\<br />
\end{array}<br />
\]
    I got the eigenvalues \lambda_1=\lambda_2=\lambda_3=0
    To find the associated eigenvectors (0I_3-A)\vec x = \vec 0
    This gives me the matrix <br />
\begin{array}{cccc}<br />
0 & -1 & -2 & 0 \\<br />
0 & 0 & -3 & 0 \\<br />
0 & 0 & 0 & 0 \\<br />
\end{array} where the last column of 0s is the augmented part of the matrix.
    This matrix is row equivalent to the identity matrix and that confuses me
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  2. #2
    MHF Contributor
    Joined
    Mar 2010
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    Florida
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    Quote Originally Posted by Jskid View Post
    Find the characteristic polynomial, eigenvalues and eigenvectors of the matrix <br />
\[<br />
A =<br />
\begin{array}{ccc}<br />
0 & 1 & 2 \\<br />
0 & 0 & 3 \\<br />
0 & 0 & 0 \\<br />
\end{array}<br />
\]
    I got the eigenvalues \lambda_1=\lambda_2=\lambda_3=0
    To find the associated eigenvectors (0I_3-A)\vec x = \vec 0
    This gives me the matrix <br />
\begin{array}{cccc}<br />
0 & -1 & -2 & 0 \\<br />
0 & 0 & -3 & 0 \\<br />
0 & 0 & 0 & 0 \\<br />
\end{array} where the last column of 0s is the augmented part of the matrix.
    This matrix is row equivalent to the identity matrix and that confuses me
    \displaystyle\begin{bmatrix}0&1&2\\0&0&3\\0&0&0\en  d{bmatrix}\Rightarrow\text{rref}=\begin{bmatrix}0&  1&0\\0&0&1\\0&0&0\end{bmatrix}

    \displaystyle\left\{\begin{bmatrix}1\\0\\0\end{bma  trix}\right\}
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