MATH 251 Midterm: MATH251 Winter 2010 Exam

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 251
• Professor: All

Document Summary

On this exam r denotes the eld of real numbers and c the eld of complex numbers. Part i. (each of these problems is worth 6 marks. : let v = m2(r), the real vector space of 2 2 matrices over r. let t : v v be de ned by. 2 = 4y1 + 3y2: (6 marks) find the general solution to the following system of di erential equations: form, (6 marks) the real matrix is in rational canonical form. 0 1 2 bd be matrices with entries from z7, and det(a) = 3, c d and b = a: (6 marks) let a = a bc. Justify. (recall: z7 is the eld with 7 det(b) = 2. If c = 5a 4c +bc + 3a. Find the value of: (6 marks) b = . H = fj(~ek) for 1 j, k 4, where (f1, f2, f3, f4) is the dual basis b of (r4) .