problemset11

# problemset11 - 12 Page 280 Problem 4 Extra Problem The...

This preview shows page 1. Sign up to view the full content.

MAS 3106 — Linear Algebra Problem Set 11 — Due 4/7/11 1. Page 256, Problem 1 2. Page 257, Problem 3b 3. Page 257, Problem 4f 4. Page 257, Problem 8 (For c, just state the result; don’t prove it) 5. Page 258, Problem 11 (for part c, use parts a and b, not the method used in class) 6. Page 259, Problem 14 7. Page 259, Problem 15 (For b, just state the result; don’t prove it) 8. Page 260, Problem 19 9. Page 260, Problem 22 (For b, just state the result; don’t prove it) 10. Page 279, Problem 2eg 11. Page 280, Problem 3d
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 12. Page 280, Problem 4 Extra Problem The minimal polynomial plays an important role in more advanced subjects of linear algebra. Definition: Let T be a linear operator on a finite-dimensional vector space. Polynomial p ( t ) is a minimal polynomial of T if (i) p ( t ) is monic and (ii) p ( T ) T and (iii) p ( t ) has smallest degree among all polynomials satisfying (i) and (ii). Prove: (a) If g ( t ) is a polynomial for which g ( T ) T , then p ( t ) divides g ( t ) . (b) The minimal polynomial of T is unique....
View Full Document

## This note was uploaded on 07/24/2011 for the course MAS 3106 taught by Professor Brigham during the Spring '11 term at University of Central Florida.

Ask a homework question - tutors are online