# Thread: Help with solving a matrix

1. ## 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

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

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

I am pretty lost as to how to compute it! I used to know how to do it..

$\displaystyle F(\lambda,\mu) =$ det $\displaystyle {|\lambda\begin{bmatrix}0 & 0 & s/2\\0 & 1 & r/2\\ s/2 & r/2 & t\end{bmatrix}}$ + $\displaystyle \mu\begin{bmatrix}-1 & 0 & 0\\0 & 0 & 1/2\\0 & 1/2 & 0\end{bmatrix}$|
=$\displaystyle -\frac{1}{4}(s^2\lambda^3 + (4t-r^2)\lambda^2\mu - 2r\lambda\mu^2 - \mu^3)$
$\displaystyle \begin{bmatrix}-\mu&0&s\lambda/2 \\ 0&\lambda&\lambda r/2 + \mu/2 \\ \lambda s/2 & \lambda r/2+\mu/2 & \lambda t \end{bmatrix}$