1. (Slide 2) find eigen values and eigen vectors for the first given matrix.

2. (Slide 2) Find eigen values and eigen vectors for the second given matrix.

3. (Slide 3) Examine manually and using Matllab the symmetric eigen decomposition, if any, for each of the matrices of (slide 2.) Are they diagonalizable? Explain your results in detail.

4. (Slide 3) Examine manually and using Matllab the symmetric eigen decomposition, if any, for each of the matrices of (slide 2.) How about the eigenspace for each case? Explain your results.

5. (Slide 4) Using given matrix for SVD on slide 4, Show all the steps of the SVD of the matrix A manually and using Matlab. Typically, the singular values arranged in decreasing order.

6. (Slide 5) Find manually and repeat using Matlab the matrix P such that E.S. x=0 is asymptotically stable for systems shown on slide 2. Assume Q=I. Explain the difficulties you confronted in finding P and how that might affect the stability.

7. Repeat for system of L(slide 4) but only using Matlab. Interpret your results and reason behind their differences. How these results differ from those of the above bullet?

8. Use (slide 6) as a guiding example.

Please show all work and verify its correctness. Also list any references.