🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeClass Notes1,200,000CA670,000

MATH136 Lecture Notes - Identity Matrix, Main Diagonal, Kazakhstani Tenge

84 views5 pages

amethystdolphin433

11 Feb 2014

School

University of Waterloo

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

harlequinminnow989 and 36957 others unlocked

$MATH136 Full Course Notes$

MATH136 Full Course Notes

Document Summary

Monday, february 3 lecture 13 : matrix multiplication. Concepts: matrix multiplication, multiplying two matrices, block-multiplying two matrices. 13. 1 definition of matrix multiplication between two matrices a and b of dimension m n and n k, respectively. 13. 1. 1 examples compute the (2, 3)th entry of the product of the given matrices d and e. 13. 1. 2 example compute the (2, 3)th entry of the product etdt for the matrices d and e above. 13. 1. 3 definition let an n = [aij] be a square matrix. The entries {a11, a22, a33, ann} is referred to as being the main diagonal of a. The matrix a is called the identity matrix of dimension n, if every element on the main diagonal of a is 1 while all others are zero. That is, aii = 1 for all i = 1 to n and aij = 0 whenever i j. The identity matrix is denoted by i or in n.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH136 Lecture Notes - Coefficient Matrix, Minuscule 22, Row And Column Vectors

amethystdolphin433

MATH136 Lecture Notes - Lecture 12: Main Diagonal, Linear Combination, Coefficient Matrix

ochresquirrel161

MATH136 Chapter Notes - Chapter 69-102: Rotation Matrix, Identity Function, Row And Column Spaces

Related Questions

can some help me with number 2 number 1 is needed to solve to get 2 please and thank you .

can some please do this for me and explain what you doing because i messed up in for the first problems causing me to do it over again can i get help on this ASAP thank you .

22

ey table is seen below xeecions tor Chapter 1 12, Fori, b â¬ Î.el * b-aa (0 (D 14 ForVEQ r the operation defined in Example 1 on the wr John Sue Henry. P iDFor 15ine if is ass ociative by determining if the final six engu defined ang property (ii)of Theorem 1 . So no element i if the operntion debined in Example 1 of Emle if each element has an inverse Section 1.3 Groups iw comutatityn ild Chapter 3 where the Funda the exercises that follow etermining why they are not Write out the Cayley table for the gru(o)nud lensify thee element the 10 elements of the group Z 18 its operation uses ts in the first coordinnte and +2 in the secotu Ldessity the Zn and write out the Cayley table. Reeall th of each element does Theorem 1.14 tell us aont the entries in the Cayley table ol s xrewp that is set with exactly one element. A {n), will always form group since there 19. What nly one way to define an operation on the set. Be sure to shhow that the properi combination of the usual notice what set the rule is be of a group all hold. 21. We can create even create groupe with games! Consider four cups placed in a ssare patter table. If we have a penny in one of the cups there are four ways we can move it to t cup: Horizontally, Vertically, Diagonally, or Stay nehere it is. We will p, S. To define nn operation, consider two movements in a row, v.e.,m ove the penny as r tells us to, then after that move the penny as y instruets. the set of integers the set of real numbers n the set of positive integers. e set of positive integers. n the set of positive integers. on the set of integers e set of negative integers. we ple, HV D since if we first move it horizontally and then vertically nltogether e moved it diagonally. Create the Cayley table for this group, identify the identity and the inverse of cach element 22. Prove that the set A 0 under matrix multiplication. Is it abelian? 23. Verify that 3(R) is a group using the addition of funetions as defined in Example 13 e set of nonzero rational n he set of nonzero real num n on the set R (-1 Section 1.4 Basic Algebra in Groups 24. Prove the Cancellation Law (Theorem 1.20). Do not use any theorems that occur after it in the text ssociative, commutative, has roof or counterexample fo 25. Assume G is a group and a e G. Consider a fixed integer k and use PMI (Theorem 0.3) to prove that for all nEN, a aYou will need to consider cases here since k can be positive, negative, or o 26. Prove Theorem 1.23 (ii) for the case of n > 0 and m