Find the two eigenvalues of a 2 × 2 symmetric matrix. Which one is closest to the (2, 2) element? Let A be the matrix in Example 6.1. For some continuous distribution in R3, generate random vectors...

Find the two eigenvalues of a 2 × 2 symmetric matrix. Which one is closest to the (2, 2) element?

Let A be the matrix in Example 6.1. For some continuous distribution in R3, generate random vectors x(i) (i = 1, ... , n)for n of at least 100, and compute ui = x(i)T Ax(i)/x(i)Tx(i). What are the maximum and minimum values of ui?