🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →
Log in
HomeStudy Guides420,000CA160,000

MATH225 : Notes Done in LaTeX

65 views47 pages
silverseal471
22 Dec 2011
School
University of Alberta
Department
Mathematics
Course
MATH225
Professor
Saeed Rahmati

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

1. 1. 2 length or norm, and unit vector . We can consider u rn as an n 1 matrix and hence ut will be a 1 n matrix u = ut =(cid:2) u1 u1 un. Note that u v is a 1 1 matrix and we can think of it just as a real number. The inner product can also be re ered to as dot product. Orthogonality u v = ut v u v =(cid:2) 1 2 (cid:3)(cid:20) 4. 6 (cid:21) u v = 4 + 12 u v = 8 v u = vt u. 2 (cid:21) v u =(cid:2) 4 6 (cid:3)(cid:20) 1 v u = 4 + 12 v u = 8. 1 u = u = (cid:2) 1 2 (cid:3)(cid:20) 1. As a result: (c1u1 + + cpup) v = c1 (u1 v) + + cp (up v) The length (or norm) of u rn is the non-negative scalar ||u|| de ned by u = .

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers

Related textbook solutions

Calculus
4 Edition,
Rogawski
ISBN: 9781319050733
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
CALCULUS:EARLY TRANSCENDENTALS
4 Edition,
Rogawski
ISBN: 9781319050740

Related Questions

5. Consider the vector space P2(R) together with inner product =P(-1),(-1) + p(0,0) + p(1)g(1). (5) (a) Use the Gram-Schmidt procedure to find an orthogonal basis for W = Span{1, x + 32²}. [5] (b) Find the orthogonal projection of 2 + 4x onto W.

please solve

Show transcribed image text

1. Let V be an inner product space. Prove the Pythagoreantheorem: if v and w E V are orthogonal then ||v+w||^2 =||v||^2 + ||w||^2. (Suggestion: start with ||v+w||^2 = (v+w,v+w).)


2. Let V=P2, the polynomials of degree less than/equal to 2 withcoefficients in R, and let (.,.): VxV -> R be the map

(p,q) = p(0)q(0) + p(1)q(1) + p(2)q(2) for any two polynomialsp(x),q(x) E V. So, for example,

(x+2, x^2-1) = (0+2)(0^2-1) + (1+2)(1^2 - 1) + (2+2)(2^2-1) =10.


a) Show that the function(.,.) defines an inner product onV.


b) Is the set A=(1,x,x^2) an orthogonal set? (with respect tothe inner product above.)


c) Is the set B=(1,x-1,3x^2-6x+1) an orthogonal set?


d) Calculate ||1||^2, and ||3x^2-6x+1||^2


e) Is the set B an orthonormal set?


f) Write f=x^2-6x+12 as a linear combination of the vectors inB.