15. Let the n x 1 random vector x have a normal density with mean vector equal to and covariance matrix equal to D,

15. Let the n x 1 random vector x have a normal density with mean vector equal to μ

and covariance matrix equal to D, where D is a diagonal matrix. Show that

$$

8[(x - \mu)'A(x - \mu)] = \sum_{i=1}^{n} a_{ii}d_i

$$

where $d_i$ is the i-th diagonal element of D.