Solve the following problem:
Given a 3 × 3 matrix Sigma:
a. Show that Sigma=cov(matrix(rnorm(30),nrow=10)) defines a proper covariance matrix.
b. Show that setting A=t(chol(Sigma)) leads to a simulation from Np(0, Σ) by using the command x=A%*%rnorm(3).
c. Compare the execution times of this approach and rmnorm when simulating one vector and 100 vectors.