MATH-205 Midterm: Bates MATH 205 111006jayawant205exam

• School: Bates College
• Department: Mathematics
• Course: MATH-205
• Professor: All

Document Summary

Name: check that you have 6 questions on two pages, show all your work to receive full credit for a problem, (12 points) short answers: (no explanations needed. If you do some calculation to get the answer, show the calculation. ) (a) find the characteristic polynomial of the matrix (cid:20) 2 1. 5 3 (cid:21). (do not solve the charac- teristic equation to nd the eigenvalues; simply nd the polynomial. ) (b) find the distance between the vector ~u = 0 (c) find the orthogonal projection of the vector ~y = . 4 and let ~u2 = is a basis for w . Then the set b = {~u1, ~u2} (e) for a 5 8 matrix a, col a = r5. What is the dimension of nul a: (10 points) let a = . If so, nd the matrices p and d so that a = p dp 1.