MATH 125 Final: MATH 125 UWashington Quiz125FinalA15

• School: UW
• Department: Mathematics
• Course: MATH 125
• Professor: All

Document Summary

Mathematical economics exam #1, september 26, 2012: let z = {z1, . , zm} be a collection of vectors in rn. De ne w = {x rn : x zi = 0, for all zi z}: show that w is not empty. Justify your answers either by proof or counter-example. Then (x + y) zi = x zi + y zi = 0 for every zi z because x, y w . This shows (x + y) w . Further, for r, ( x) zi = (x zi) = 0 for every zi z because x w . Since the sum of any two vectors in w is in w and any scalar multiple of a vector is w is in w rn, w is a vector subspace of rn. Answer: the set is open: prove your answer in part (a).