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Math Help - Help with solving a matrix

  1. #1
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    Help with solving a matrix

    I forget how to compute the following matrices. Is there a formula that I should be using to compute this? Thanks

    F(\lambda,\mu) = det {|\lambda\begin{bmatrix}0 & 0 & s/2\\0 & 1 & r/2\\ s/2 & r/2 & t\end{bmatrix}} + \mu\begin{bmatrix}-1 & 0 & 0\\0 & 0 & 1/2\\0 & 1/2 & 0\end{bmatrix}|

    = -\frac{1}{4}(s^2\lambda^3 + (4t-r^2)\lambda^2\mu - 2r\lambda\mu^2 - \mu^3)

    I am pretty lost as to how to compute it! I used to know how to do it..
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  2. #2
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    Quote Originally Posted by shadow_2145 View Post
    I forget how to compute the following matrices. Is there a formula that I should be using to compute this? Thanks

    F(\lambda,\mu) = det {|\lambda\begin{bmatrix}0 & 0 & s/2\\0 & 1 & r/2\\ s/2 & r/2 & t\end{bmatrix}} + \mu\begin{bmatrix}-1 & 0 & 0\\0 & 0 & 1/2\\0 & 1/2 & 0\end{bmatrix}|

    = -\frac{1}{4}(s^2\lambda^3 + (4t-r^2)\lambda^2\mu - 2r\lambda\mu^2 - \mu^3)

    I am pretty lost as to how to compute it! I used to know how to do it..
    Just add up the matrices:
    \begin{bmatrix}-\mu&0&s\lambda/2 \\ 0&\lambda&\lambda r/2 + \mu/2 \\ \lambda s/2 & \lambda r/2+\mu/2 & \lambda t \end{bmatrix}

    Now apply the definition for finding determinants.
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