MATH 271 Final: MATH 271 Amherst F16M271 2802 29FinalChing

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 271
• Professor: All

Document Summary

Wednesday 21 december: (5 points) prove that, for any vector space v , the equation 1. 2 (v + v) = v holds for all v v . (you should every step of your answer with reference to the axioms in the de nition of a vector space. You may not assume additional facts about vector spaces beyond the axioms. : (5 points each) in each of the following cases, decide if w is a subspace of v or not. , vn} be a basis of v . Prove that t is injective if and only if {t (v1), . , t (vn)} is linear independent: (10 points) calculate the dimension of the subspace of r4 determined by the equations. 2x1 + x2 3x3 + x4 = 0. Justify your answer. (b) for each of your answers to part (a), give an example of a linear transformation.