MATH 240 Midterm: MATH240 BOYLE-M SPRING2013 0101 MID SOL 1

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

Document Summary

Math 240 spring 2013 exam 3 solutions. 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: (20 points) let a = . Find a diagonal matrix d and an invertible matrix p such that p 1ap = d. (do not compute p 1. ) Because a is triangular, its eigenvalues are the diagonal entries 1, 2, 0. For each eigenvalue , solve (a i)x = 0 to get an eigenvector for . We let the columns of p be the eigenvectors and d the diagonal matrix with their eigenvalues: 0 0 0: (21 points) determine which of the following matrices are diagonaliz- able: