MATH 240 Final: MATH240 BOYLE-M SPRING2013 0101 FINAL EXAM

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

Document Summary

Math 240 spring 2013 final exam. Answer each 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: (a) (25 points) the following matrices are row equivalent: Then t is a linear trans- formation: (a) (10 points) suppose a, b, c are invertible 3 3 matrices and as a partitioned matrix (block matrix) the 6 6 matrix u has the form u = (cid:18)a 0. Find the block matrix form for u 1. (b) (15 points) let t : r2 r2 be the linear transformation which rotates a vector counterclockwise around the origin by 5 /4 radians and then multiplies its length by 3. Prove that ||u z|| = ||z|| : suppose x and y are vectors in rn.