s11week06

s11week06 - Math 205, Spring 2011 Homework 6: due Feb 28...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 205, Spring 2011 Homework 6: due Feb 28 (Mon) Chapter 4, Sections 3, 4 and 5. Week 6: 4.3 Subspaces/Nullspace 4.4 Spanning Sets 4.5 Linear Dependence, Linear Independence Recall that a Vector Space V may be any collection with formulas for vector plus and scalar mult, V = ( V , + , ) with 10 rules. In practice, in Math 205, Vector Spaces will usually be subsets of one of four standard Examples: R n ; V = M m n ( R ); C k ( a, b ) = functions: f+g, k f, 0, -f with k derivatives P n = polynomials with real coef. degree < n. 2 We usually assume the 10 rules for these four vector spaces (the rules are easier to verify than to remember). So to establish that a subset S of one of these spaces is a vector space we only need to check the last two rules, in which case we say that S is a Subspace of V. The two subspace conditions are the closure rules (1) for every vectoru,vectorv S, check vectoru + vectorv S (closure under vector +), and (2) for every vectoru S, and every scalar c R , check cvectoru S (closure under scalar mult). For the formal definition of span and spanning set we take vectors vectorv 1 ,vectorv 2 , . . . ,vectorv k in a vector space V. For the most part,...
View Full Document

Page1 / 5

s11week06 - Math 205, Spring 2011 Homework 6: due Feb 28...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online