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Math Help - Does matrix AS=SD?

  1. #1
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    Does matrix AS=SD?

    This is part of a bigger question, though I've answered much of the parts before this part. I'll list the data before I list the question.

    A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}
    S=\begin{bmatrix}1 & 1 & 0\\1 & 0 & 1\\1 & -1 & -1\end{bmatrix}
    (The columns of S are the eigenvectors of A, just to note)

    Now onto the question.

    Let D be the diagonal matrix whose entry d_i is the eigenvalue corresponding to column i of S. Compute SD. Does AS=SD?

    It's probably not that hard, but I'm a little short on time due to other matters. I'm also not sure whether or not there was a typo on the question we were given.
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  2. #2
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    Quote Originally Posted by Runty View Post
    This is part of a bigger question, though I've answered much of the parts before this part. I'll list the data before I list the question.

    A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}
    S=\begin{bmatrix}1 & 1 & 0\\1 & 0 & 1\\1 & -1 & -1\end{bmatrix}
    (The columns of S are the eigenvectors of A, just to note)

    Now onto the question.

    Let D be the diagonal matrix whose entry d_i is the eigenvalue corresponding to column i of S. Compute SD. Does AS=SD?

    It's probably not that hard, but I'm a little short on time due to other matters. I'm also not sure whether or not there was a typo on the question we were given.


    Well, as there are three lin. ind. eigenvectors of A (this follows from calculating the determinant of S), we know that S^{-1}AS=D ...and from here you can solve the question .

    Tonio
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