MTH 162 Midterm: MTH 162 University of Rochester 162 Spring 2007 Midterm 1

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Petridis: no calculators are allowed on this exam. 1: (16 points) (a) find two disjoint nite spanning sets for the following subspace of r3: W = {(x, y, z) r3 : x + y + z = 0}. Recall that two sets are disjoint when they have no element in common. Show all your work and/or justify your answer brie y. (b) find a nite spanning set for the subspace. U = {(x, y, z) : 2x y = 0} that contains precisely one element from w . Show all your work and/or justify your answer brie y. 2: (17 points) (a) let v be a 5-dimensional vector space over r, and let t : v v be a linear trans- formation. Prove that it is impossible to have n (t ) = r(t ). Let v = r3 and consider the subset. 4: (17 points) let t : r3 7 r3 be a linear map.