assignment1

# assignment1 - School of Engineering Science ENSC 483 Modern...

This preview shows pages 1–2. Sign up to view the full content.

School of Engineering Science ENSC 483 - Modern Control Systems Spring 2007–Assignment I (Warm-up Homework!) 1. Use Laplace’s Expansion to evaluate the determinants of the following matrices: A = 3 0 1 2 4 3 1 1 2 ; B = 1 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7 2. Find the inverse of matrices in problem 1. 3. (a) You are told that matrices A , and B are symmetric and that their product is symmetric. What can you conclude from this? (b) A matrix is called idempotent if A 2 = A . Consider the case of 2 × 2 idempotent matrices and say as much as you can about them, and based on your arguments give an example of a 2 × 2 idempotent matrix. 4. Show that the set of all real n × n matrices with usual operation of matrix addition and the usual operation of multiplication of matrices by scalars constitutes a vector space over the reals (i.e., < n × n , < ). Determine dimension and a basis for this space. Is the above statement still true if ( < n × n , < ) is replaced by ( < m × n , <

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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