MATH 240 Midterm: MATH240 BOYLE-M FALL2012 0101 MID EXAM 2

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

Document Summary

Answer each 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 a short nal answer, put a box around that answer. Notation: if a is a matrix, then at denotes the transpose of a: (a) (20 points) let a = (cid:18)5 7. Write down a matrix u and a diagonal matrix d such that u 1au = d. (b) (4 points) give an example of a 2 2 matrix b which has a real eigenvalue and is not diagonalizable. No proof necessary: (18 points) there is a change of variable, x = p y, that transforms the quadratic form q(x) = x2. 2 into a quadratic form with no cross term. (in other words, with x = p y, there are numbers , such that q(x) = y2. What is the symmetric matrix a such that q(x) = xt ax ? (b) (6 pts. )