MATH 240 Final: MATH240 BOYLE-M SPRING2012 0101 FINAL EXAM

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

Document Summary

Math 240 spring 2012 final exam. *** there are questions on both sides of this paper *** Answer each question on a separate sheet of paper. On each sheet, put your name and your section ta and meeting time. You may assume given matrix equations are well de ned (i. e. the matrix sizes are compatible). If your nal answer is short, put a box around it: for x = (x1, x2) in r2, de ne q(x) = 4(x1)2 + 6x1x2 + 3(x2)2. (a) (15 pts. ) Determine whether this quadratic form is positive de nite, positive semide nite, negative de nite, negative semide nite or inde nite. Subject to the constraint ||x|| = 1, what is the minimum value of q(x)? (c) (15 pts. ) The vectors (cid:0)1 2 3(cid:1) ,(cid:0)1 2 4(cid:1) and (cid:0)2 1 1(cid:1) are the corners of a tri- angle t in r3. What is the area of t : (a) (30 pts. )