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Math Help - Finding Determinent of a Matrix

  1. #1
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    Finding Determinent of a Matrix

    I have a matrix:

    \begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}

    I believe I've correctly used cofactor expansion to get:
    (x-5)^(3+3) det( \begin{bmatrix}x-4&4\\-1&x \end{bmatrix})
    I'm not sure what to do from this point, or if I'm doing it correctly at all... Help appreciated.
    For instance, how would I find the cofactor of the new matrix?
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    I have a matrix:

    \begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}

    I believe I've correctly used cofactor expansion to get:
    (x-5)^(3+3) det( \begin{bmatrix}x-4&4\\-1&x \end{bmatrix})
    I'm not sure what to do from this point, or if I'm doing it correctly at all... Help appreciated.
    For instance, how would I find the cofactor of the new matrix?
    Why is (x-5) raised to the power of (3+3)?

    "I'm not sure what to do from this point, ..." You should know how to get the determinant of a 2x2 matrix.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Why is (x-5) raised to the power of (3+3)?

    "I'm not sure what to do from this point, ..." You should know how to get the determinant of a 2x2 matrix.
    Sorry, I meant to raise (-1) to (3+3).
    (x-4)(4)-(4)(-1)
    4x-16+4
    (x-5)(4x-12)

    Do I equate that to zero or something?
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  4. #4
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    <br />
\begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}<br />

    Could you do it like this:

    (x-4)(x)(x-5)+4(x-5)=x(x^2-9x+20)+4x-20=x^3-9x^2+24x-20

    ?

    You can try and factorise it if you like.
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