New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Applied Linear Algebra

by: Mary Veum

Applied Linear Algebra MATH 2210

Mary Veum
GPA 3.97

Thomas Roby

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Thomas Roby
Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 6 page Class Notes was uploaded by Mary Veum on Thursday September 17, 2015. The Class Notes belongs to MATH 2210 at University of Connecticut taught by Thomas Roby in Fall. Since its upload, it has received 25 views. For similar materials see /class/205825/math-2210-university-of-connecticut in Mathematics (M) at University of Connecticut.

Similar to MATH 2210 at UCONN

Popular in Mathematics (M)


Reviews for Applied Linear Algebra


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/17/15
21 Matrix Operations Matrix Notation Two ways to denote m x n matrix A In terms of the columns ofA In terms of the entries ofA all 611 01quot A ah ay am an amj amquot Main diagonal entries Zero matrix 0 0 0 0 0 0 0 0 0 0 THEOREM 1 LetA B and C be matrices ofthe same size and let r and s be scalars Then aABBA drABrArB bABCABC ersArAsA CA0 A f rsA rsA Matrix Multiplication Multiplying B and X transforms X into the vector BX In turn if we multipIyA and BX we transform Bx into ABX SoABX is the composition of two mappings De ne the product1B so thatABx ABX SupposeA is m x n and B is n Xp where 961 962 B b1 b2 bpandx xp Then BX x1b1x2b2 prp and ABXAx1b1x2b2 prp Ax1b1 Ax2b2 Aprp x1 xlAb1szb2prbp Abz xz xp Therefore and by de ning AB Ab1 Abz Abp we have ABx ABX 472 375 01 EXAMPLE Compute AB whereA Solution gtAB andB 273 677 4 72 Abz 3 75 3 0 1 77 2 26 77 74 2 724 26 6 77 Note thatAb1 is a linear combination ofthe columns ofA and Abz is a linear combination of the columns ofA Each column ofAB is a linear combination ofthe columns ofA using weights from the corresponding columns ofB EXAMPLE lfA is 4 x 3 and B is 3 x 2 then what are the sizes ofAB and BA Solution gtllt gtllt BAwould be gtllt gtllt which is lfAismxnandBisnxpthenABismgtltp RowColumn Rule for Computing AB alternate method The definition AB Ab1 Abz wAbp is good for theoretical work When A and B have small sizes the following method is more efficient when working by hand fAB is defined let ABy denote the entry in the ith row and jth column ofAB Then anblj 612sz ambnj an 612 am 143 2 73 2 3 6 EXAMPLE A B 0 1 ComputeAB if it is de ned 71 0 1 4 77 Solution Since A is 2 x 3 and B is 3 x 2 then AB is defined and AB is x 2 73 2 73 2 3 6 28 I 2 3 6 28 745 AB 0 1 0 1 71 0 1 I I 71 0 1 I I 4 77 4 77 2 73 2 73 2 3 6 28 745 2 3 6 28 745 0 1 0 1 71 0 1 2 I 71 0 1 2 4 4 77 4 77 28 745 SoAB 2 74 THEOREM 2 LetA be m x n and let B and C have sizes for which the indicated sums and products are defined a ABC ABC associative law of multiplication b AB C AB AC left distributive law c B CA BA CA rightdistributive law d rAB rAB ArB for any scalar r e MA A A1quot identity for matrix multiplication WARNINGS Properties above are analogous to properties of real numbers But NOT ALL real number properties correspond to matrix properties 1 It is not the case thatAB always equal BA see Example 7 page 114 2 Even ifAB AC then B may not equal C see Exercise 10 page 116 3 It is possible forAB 0 even ifA 0 and B 0 see Exercise 12 page 116 Powers ofA Ak AA EXAMPLE liilliilliilliill lliillziil lfA is m x n the transpose ofA is the n x m matrix denoted byAT whose columns are formed from the corresponding rows ofA EXAMPLE 167 12345 276 A 67898 2 AT385 76543 494 583 1 2 1 2 0 EXAMPLE LetA 3 0 1 B 0 1 ComputeAB ABTATBTand BTAT Solution 120 12 AB 01 3 01 724 ABT 13 10 2 7 310 ATBT 20 2074 214 01 214 10 2 13 BTAT 7 1 1 214 01 THEOREM3 LetA and B denote matrices whose sizes are appropriate for the following sums and products a ATT A Le the transpose ofAT is A b A BT ATBT c For any scalar r rAT rAT d ABT BTAT le the transpose ofa product of matrices equals the product oftheir transposes in reverse order EXAMPLE Prove that ABCT Solution By Theorem 3d ABCV ABCT CT T CT


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.