Let A ∈ R^m,n be a matrix. Assume that u ∈ Rⁿ is a vector-valued random variable, with zero mean and covariance matrix I_n. That is, E{u} = 0, and E{uu^T} = I_n.

1. What is the covariance matrix of the output, y = Au?

2. Define the total output variance as is the output’s expected value. Compute the total output variance and comment.

E {|ly - 9||2}, where 9 = E{y}