If Gaussian random vector has singular covariance matrix, isn't there probability density function?

Question

I got a complicated problem. Suppose that Gaussian random vector having Covariance matrix; $$K_X=\left[\begin{matrix}1 &-\frac12 &-\frac12 \\ -\frac12 &1 &-\frac12 \\ -\frac12 &-\frac12 &1\end{matrix}\right]$$ It is clearly singular since $\mathrm{det}|K_X|=0.$ However problem maker told me that find out that Gaussian pdf but I know that Jointly Gaussian pdf equation includes the inverse matrix of $K_X$ but in our case, there is no inverse matrix since $K_X$ is singular. Do I really find out pdf nothing? Let me ask you question. Thank you.