(b The variances of random variables Y and Z are 0.36 and 16 respectively, the covariance Cov(Y, Z) = 2. (i) Write down the variance-covariance matrix A of (Y, Z) vector. (ii) Verify that the eigenvalues for the matrix A are: M = 16.25171, 22= 0.108295. Verify that the corresponding eigenvectors are: x1 = (1, 7.945855), x2= (1, -0.1258525). Hint: Verify that the eigenvalues are solutions for equation (2). Alternatively, just solve the equation (2). Write down the equation to solve for scalars a (A - Al)x = 0, (1) where I is 2 x 2 identity matrix; hence, det (A -21)=0, (2) recall for any 2 X 2 matrix C = C11 LC21 C22 det(C) = C11C22 - C12 C21 Thus rewrite eq. (2) in the following form (all - 1)(a22 - 2) - a12a21 = 0 (3) Then for validation of the pairs of eigenvalues and eigenvectors substitute the eigenvalues into eq. (3) and the eigenvectors into eq. (1), respectively