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Math Help - Eugen Values for matrix

  1. #1
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    Question Eugen Values for matrix

    I have the following 2x2 matrix:
    (1-A) 1
    1 (5-A)

    I need to solve to get the Eigen values. How do i develop the quadratic eqn from that to solve for A?
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  2. #2
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    If I understand correctly, we have the matrix A=\begin{bmatrix}1&1\\1&5\end{bmatrix}

    we can find the eigenvalues by \begin{bmatrix}1-{\lambda}&1\\1&5-{\lambda}\end{bmatrix}

    The characteristic polynomial is given by Det({\lambda}I-A)

    Det\left({\lambda}\cdot\begin{bmatrix}1&0\\0&1\end  {bmatrix}-\begin{bmatrix}1&1\\1&5\end{bmatrix}\right)

    ={\lambda}^{2}-6{\lambda}+4

    Solve the quadratic to find the eigenvalues.
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  3. #3
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    But how did you get the 6 and 4?
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  4. #4
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    Question

    hmm
    So i get the determinant:
    (1 - A)(5 - A) - (1)(1)

    but how do i get to the next step?
    A^2 - 6A + 4
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by taurus View Post
    hmm
    So i get the determinant:
    (1 - A)(5 - A) - (1)(1)

    but how do i get to the next step?
    A^2 - 6A + 4
    Common algebra. Expand the bracket and simplify.

    CB
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