312S13FEx-c

B4 say vectorx t is a solution of dvectorx dt

• Notes
• 2

This preview shows page 2 out of 2 pages.

B–4. Say vectorx ( t ) is a solution of dvectorx dt = Avectorx , where A := parenleftbigg c 5 5 c parenrightbigg . For which value(s) of the real constant c does every solution vectorx ( t ) tends to zero as t → ∞ ? B–5. Of the following three matrices, which (if any) can be orthogonally diagonalized; which can be diagonalized (but not orthogonally); and which cannot be diagonalized at all. Identify these fully explaining your reasoning. A = 0 2 3 2 0 2 3 2 0 , B = 0 3 1 0 0 2 0 0 0 , C = 7 1 3 0 1 1 0 0 2 B–6. Let A := 1 0 1 1 0 1 . By a routine computation the matrix A A = parenleftbigg 2 1 1 2 parenrightbigg has eigen- values 3 and 1 with corresponding eigenvectors parenleftbigg 1 1 parenrightbigg and parenleftbigg 1 1 parenrightbigg , a) Use this to find the singular value decomposition of A . b) Find the best rank 1 approximation to A . 2

{[ snackBarMessage ]}

"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern