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Thread: How can i prove that about Det(a1,,an)?

  1. #1
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    How can i prove that about Det(a1,,an)?

    -matrix.png
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  2. #2
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    Re: How can i prove that about Det(a1,,an)?

    Try using Gaussian elimination to transform this matrix to an upper diagonal one. Then read the determinant off as the product of the diagonal elements.
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  3. #3
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    Re: How can i prove that about Det(a1,,an)?

    some hints

    Look at the matrix $\displaystyle B=A-xI$ where $\displaystyle I$ is the $\displaystyle n\times n$ identity matrix

    the characteristic polynomial of $\displaystyle B = det(B-xI)$

    $\displaystyle B$ is a rank one matrix
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  4. #4
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    Re: How can i prove that about Det(a1,,an)?

    Quote Originally Posted by Idea View Post
    some hints

    Look at the matrix $B=A-xI$ where $I$ is the $n\times n$ identity matrix

    the characteristic polynomial of $B = det(B-xI)$

    $B$ is a rank one matrix
    I have replace "tex" with dollar signs.
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