Multiline equations using IEEEtrantools when also using \left \lbrack and \left \{

Question

I have a set of code in which I have

\begin{IEEEeqnarray*}{rCl}
f(y,x) & = & \frac{1}{(2\pi)\left | \Sigma_{xx} \right |^{\frac{1}{2} \cdot
       \left | (\Sigma_{yy} - \Sigma_{yx}\Sigma_{xx}^{-1}\Sigma_{yx}^{\prime})^{-1} \right |^{\frac{1}{2} \\
&& \cdot exp \left \{ -\frac{1}{2} \left \lbrack (y - \mu_y)^{\prime} (\Sigma_{yy} - \Sigma{yx}\Sigma_{ya}\Sigma_{xx}^{-1}\Sigma_{yx}^{\prime})^{-1}(y - \mu_y) \\
&& -(x - mu_x)^{\prime}\Sigma_{xx}^{-1}\Sigma_{yx}^{\prime} (\Sigma_{yy} - \Sigma_{yx}\Sigma_{xx}^{-1}\Sigma_{yx}^{\prime})^{-1}(y-\mu_y) \right \rbrack \right \}

It works if I put it under the second line but not the third.

Any suggestions much appreciated.