Subject:Discrete Mathematics 2d Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are(1 0 1 0)0 1 0 1(1 0 1 0)1 0 0 1M, =and MFind the matrices of1 0 1 00 1 0 10 11 00 1(i)RUS,(ii)Ro S,(iii)(S o R)".

let A=a,b,c,d and let R and S be the relations on A whose matrices are MR=1010010110100101 and…

Answered: Let A = {a, b, c, d} and let R and S be…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 33E

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Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.
Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. Sec. 3.3,22b,32b Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .
Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?

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Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0` 0 1 0 1 (1 0 1 0` 1 0 0 1 0 1 1 0 0 1 0 1 MR and Ms . Find the matrices of %3! 10 1 0 0 1 0 1) (i) RUS, (ii) Ro S, (ii) (S • R)'.