This is a followup question from the previous post, where the following multivariate distribution function is given by:
$$\exp(-\frac12 \vec x^T\Sigma^{-1}\vec x)$$
Now, it was mentioned in the comments that if the $\Sigma$ was singular, such as follows:
$$\begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}$$
then the
"distribution function however will be singular, having infinite weight along the diagonal and zero weight everywhere else"
I want to mathematically see how this is the case? How the diagonal is infinite weight and how the off diagonal are all 0's