lect136_11_w09

lect136_11_w09 - Wednesday, January 28 - Lecture 11 :...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Wednesday, January 28 Lecture 11 : Subspaces II . (Refers to section 3.4) Expectations : 1. Determine if a given subset of R n is a subspace. 2. Given a subspace W of R n define the orthogonal complement W of W and show it is a subspace. 3. Show that for W = span{ v 1 , v 2 , . ., v m } in R n , x W iff < v i , x > = 0 for all i = 1 to m . 11.1 Theorem If U and W are two subspaces of R n then U W, (the set of all the elements they have in common), is subspace of R n . Proof : o The set U W is non-empty. (Why?) o Let v and w be any two vectors in U W , and let α and β be a scalars. (The two vectors v and w may be the same vector.) o Then belongs to both U and W . o Since both U and W are subspaces then α v + β w belongs to both U and W . So α v + β w belongs to U W and so is a subspace of R n . 11.2 Exercise – Is the set S = {( a , b , – b , c ) : a , b , c in R } a subspace of R 4 ? Find a spanning family for S (if there is one). Solution outline:
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/04/2009 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

Page1 / 3

lect136_11_w09 - Wednesday, January 28 - Lecture 11 :...

This preview shows document pages 1 - 2. Sign up to view the full document.

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