Linear algebra homework. Please help me

5.3.1 Computer Projects EXERCISES 1. Try the MATLAB command [B,D]=cig(A), where A is as in Example 5.10 on page 298. This demonstrates that MATLAB knows about complex eigenvalues. 2. A complex matrix A is Hermitian symmetric if A* - A. Give an example of a 3 x 3 Hermitian matrix. Keep all entries nonzero and use as few real entries as possible. Enter your matrix into MATLAB. (Complex numbers such as 2 + 3/ 306 EIGENVECTORS AND EIGENVALUES are entered into MATLAB as 2+3*i.) Then get MATLAB to find the eigenvalues. They are all real! 3. Change one of the entries of the matrix A from Exercise 2 to make it non- Hermitian. Are the eigenvalues still real?EXAMPLE 5.10 1 + V3/ F-2 FIGURE 5.3 Example 5.9. COMPLEX EIGENVECTORS 299 Compute A20 where Solution. This problem looks very much like some problems that we solved in Section 5.2. The technique was to diagonalize A. Specifically, we found a diagonal matrix D and an invertible matrix O such that A = ODO-. Then Theorem 5.4 on page 287 in Section 5.2 shows that A20 - OD"Q-1. To find Q, we need to find the eigenvalues of A. We compute 17 21-2-21+4 Using the quadratic formula, we find 1 2+ V4-16 2 Now we are concerned-the roots are complex. Let us, however, proceed with our computation and see what happens. To find the eigenvectors, we must solve the equation (A - 2/)X =0. Assume first that A - 1 + V3i. Then our equation is -V3i This corresponds to the system