how to prove this statement for all sum of cov positive?

Question

Let $X_1, ..., X_n$ be some random variables and let $c_{ij} = cov(X_i, X_j)$. Show that for any numbers $a_1, ..., a_n$, we have $$\sum\limits_{i=1}^n \sum\limits_{j=1}^n a_ic_{ij}a_j \geq 0$$.

Answer 1

Hint:

Covariance matrix is positive semidefinite.