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Math Help - [SOLVED] Invertible and diagonal matrix

  1. #1
    Member mybrohshi5's Avatar
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    [SOLVED] Invertible and diagonal matrix

    Let A =  \begin{bmatrix}3&-\frac{1}{2}\\-6&5 \end{bmatrix}

    Find an invertible S and a diagonal D such that S^{-1}AS = D

    S =  \begin{bmatrix}.&. \\.&. \end{bmatrix}

    D =  \begin{bmatrix}.&.\\.&. \end{bmatrix}


    I have never seen a problem like this and i am just a little confused on where to begin..

    Thank you for any help
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mybrohshi5 View Post
    Let A =  \begin{bmatrix}3&-\frac{1}{2}\\-6&5 \end{bmatrix}

    Find an invertible S and a diagonal D such that S^{-1}AS = D

    S =  \begin{bmatrix}.&. \\.&. \end{bmatrix}

    D =  \begin{bmatrix}.&.\\.&. \end{bmatrix}


    I have never seen a problem like this and i am just a little confused on where to begin..

    Thank you for any help
    on the main diagonal of D put the eigenvalues of A and the columns of S are the eigenvectors corresponding to the eigenvalues of A.
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  3. #3
    Member mybrohshi5's Avatar
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    This is what i got but it says it is wrong.

    for my eigenvalues i got

    \lambda_1 = 2 and \lambda_2 = 6

    from my eigenvalue of \lambda_1 = 2 i got the eigenvector of
     \begin{bmatrix}\frac{1}{2}\\1\end{bmatrix}

    from my eigenvalue of \lambda_2 = 6 i got the eigenvector of
     \begin{bmatrix}\frac{1}{6}\\1\end{bmatrix}

    so for my S matrix i got

    S = \begin{bmatrix}\frac{1}{2}&\frac{1}{6} \\ 1&1\end{bmatrix}

    D = \begin{bmatrix}2&0\\0&6\end{bmatrix}

    Can you see what i did wrong?

    Thanks for the help
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  4. #4
    Member mybrohshi5's Avatar
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    Never mind i got it. the 1/6 is supposed to be a -1/6

    Thanks again for the help
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