MATH 240 Final: MATH240 BOYLE-M SPRING2011 0101 FINAL SOL

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

Document Summary

Math 240 spring 2011 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: (20 points) determine whether the quadratic form. Q(x1, x2) = 200(x1)2 200x1x2 51(x2)2 is positive de nite, positive semide nite, negative de nite, negative semide nite, or inde nite. Here the trace of a is negative and the determinant of a is positive. Therefore both eigenvalues are negative,and q is negative de nite. (alternately, you can compute the characteristic polynomial of a to be t2 + 251t + 200 and then use the quadratic formula to see that its two roots.