Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)

13th Edition

ISBN: 9780321947628

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Textbook Question

Chapter 4.4, Problem 31E

Problems 31 - 48 refer to the following matrices:

A = 2 0 − 1 4 3 − 2 B = − 3 1 2 5 C = − 1 0 2 4 − 3 1 − 2 3 5 D = 3 0 1 − 2 − 1 2

A C

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Chapter 4.4, Problem 30E

Chapter 4.4, Problem 32E

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= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.

(a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001

(a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b²=ab = ba 0. (ii) a² (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.

Chapter 4 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)

Ch. 4.1 - Can a consistent and dependent system have exactly...Ch. 4.1 - Return to Example 2 and solve each system by...Ch. 4.1 - Solve by graphing and check: 2xy=3x+2y=4 Ch. 4.1 - Solve each of the following systems by graphing:...Ch. 4.1 - Solve to two decimal places using graphical...Ch. 4.1 - Solve by substitution: 3x3y=22xy=6 Ch. 4.1 - Solve the following system using elimination by...Ch. 4.1 - Dennis wants to use cottage cheese and yogurt to...Ch. 4.1 - Find the equilibrium quantity and equilibrium...Ch. 4.1 - In Problems 1-6, find the x and y coordinates of...

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Problems 31 - 48 refer to the following matrices: A = 2 0 − 1 4 3 − 2 B = − 3 1 2 5 C = − 1 0 2 4 − 3 1 − 2 3 5 D = 3 0 1 − 2 − 1 2 A C

Solution Summary: The author calculates the product AC, where A=left[cc2& -1& 3 0& 4&

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