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Math Help - Eigenvectors

  1. #1
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    Unhappy Eigenvectors

    The matrix i have is |3 4| |4 -3| How do I find the corresponding eigenvectors? 2x2 matrix. 1st row 3 4, 2nd is 4 -3.
    I have done the first step of the process, and found eigenvalues of +-5. Now how do I find the eigenvectors? I have aksed this question before, and I have recieved help which I already know how to do. When I substitue in the eigenvalues to find the eigenvectors, I get x1=0 and x2=0, so there must be some other way to find the eigenvector. If possible, find a final solution to the problem so I know the method works. Thanks
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  2. #2
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    Quote Originally Posted by LooNiE View Post
    The matrix i have is |3 4| |4 -3| How do I find the corresponding eigenvectors? 2x2 matrix. 1st row 3 4, 2nd is 4 -3.
    I have done the first step of the process, and found eigenvalues of +-5. Now how do I find the eigenvectors? I have aksed this question before, and I have recieved help which I already know how to do. When I substitue in the eigenvalues to find the eigenvectors, I get x1=0 and x2=0, so there must be some other way to find the eigenvector. If possible, find a final solution to the problem so I know the method works. Thanks
    \lambda = 5: \left( \begin{array}{cc}<br />
3 & 4 \\<br /> <br />
4 & -3\end{array}\right) \left( \begin{array}{c}<br />
x \\<br />
y \end{array}\right) = 5 \left( \begin{array}{c}<br />
x \\<br />
y \end{array}\right)

    Therefore:

    3x + 4y = 5x \Rightarrow x = 2y .... (1)

    4x - 3y = 5y \Rightarrow x = 2y .... (2)

    Therefore the corresponding eigenvector has the form \left( \begin{array}{c}<br />
2y \\<br />
y \end{array}\right) = y \left(\begin{array}{c}<br />
2 \\<br />
1 \end{array}\right) and so the eigenvector is \left( \begin{array}{c}<br />
2 \\<br />
1 \end{array}\right).

    Do the same thing for \lambda = -5.
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