This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (in another math book or on the internet). a. Prove that ∼ W is an equivalence relation. We denote the set of equivalence classes by the symbol V/W . b. For v ∈ V , let [ v ] denote its equivalence class in V/W . De±ne an addition rule ˜ + on V/W by [ u ] ˜ +[ v ] = [ x + y ] , where x ∈ [ u ] , y ∈ [ v ] , and + is the usual addition in V . Prove that this addition on equivalence classes is wellde±ned, and that it does not depend on the choices of x and y . c. Come up with a de±nition of scalar multiplication on V/W , and show that it is wellde±ned. d. Prove that V/W is a vector space over R . e. Let V = R 3 and W those vectors x y z ∈ R 3 satisfying x + y + z = . Prove that R 3 /W is onedimensional....
View
Full
Document
This homework help was uploaded on 02/24/2008 for the course MATH 2240 taught by Professor Taraholm during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 TARAHOLM

Click to edit the document details