MATH 240 Midterm: MATH240 BOYLE-M SPRING2012 0101 MID SOL

• School: University of Maryland
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

Math 240 spring 2012 exam 3. Answer each question on a separate sheet of paper. On each sheet, put your name, your section leader"s name and your section meeting time. When a question has short nal answer, put a box around that answer: (20 points) let a = (cid:18)3 5. Write down a matrix u such that u 1au is a diagonal matrix. = 8 is an eigenvalue of a with eigenvector (cid:18)1. The other eigenvalue is -4 (because the sum of the two eigenvalues is the trace, 3 + 1; or, by computing the characteristic polynomial and its roots). An eigenvector for = 4 is a nonzero solution of (a ( 4i))x = 7 5(cid:19), an eigenvector for = 4 is (cid:18) 5. 7 (cid:19): since a ( 4i) = (cid:18)7 5. Therefore we can use u = (cid:18)1 5.