MATH 240 Midterm: MATH240 BOYLE-M SPRING2011 0101 MID SOL

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

Document Summary

Math 240 spring 2011 exam 1. *** there are questions on both sides of this paper *** Answer each question on a separate sheet of paper. On each sheet, put your name, your section leader"s name and your section meeting time. You must be careful on arithmetic check. No proof is needed for true-false questions; just write clearly. You may assume given matrix equations are well de ned (i. e. the matrix sizes are compatible): (10 points) (a) (5 pts. ) Let t : r2 r2 be de ned by t (x) = y, where y1 = x1 + 3x2 and y2 = x2 1. Prove that t is not a linear map. Solution: we have t (0) = (cid:18) 0. If t is linear, then t (0) = 0, so our t (b) (5 pts. ) Solution: the columns will span r2 for any h except h = 6.