My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

Thanks Tree1Thanks
  • 1 Post By skipjack
LinkBack Thread Tools Display Modes
July 4th, 2018, 11:28 PM   #1
Joined: Jul 2018
From: india

Posts: 1
Thanks: 0

Post Immediate Help Required in discrete mathematics

Hi Friends,

I am new to this forum and my son is awfully struck in some discrete mathematics question. Your help is highly solicited. The questions are posted below:

1. Prove that if H, K are subgroups of a group G and H Ų K = G. Then either H=G or K=G

2. Let G be a group and a, b Є G. Then the equation x*a=b has a unique solution given by x= b* a

3. Linear sum W1+ W2 of two subspaces W1and W2 of a vector space V(F) is A subspace of V(F)

4. show that the function T: R2 → R2 such that T(0,1)=(3,4),T(3,1)=(2,2) And T(3,2)=(5,7) is not a L.T.

5. Let T:v →w be a linear transformation. Then T is onto iff p(T)= dim w.

6. show that the function T: R2 → R2 defined by T(x1,x2)=(x1-x2,x1+x2),for (x1,x2)Є R2 is bijective

Please provide detailed steps as I do not know these mathematics, but when I give this to my son, he can understand. Thanks in advance friends.
Meghhiya is offline  
July 5th, 2018, 02:15 AM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,919
Thanks: 2202

2. For a, b ∈ G, where (G,*) is a group, let c ∈ G be the unique inverse of a,
then x*a = b implies (x*a)*c = b*c, which simplifies to x = b*c.

Note: the usual axioms of a group (G,*) specify that the group operation is associative and that each element of G has an inverse. It's an elementary theorem that no element has more than one inverse.

4. If T is a L.T., T(0,1) + T(3,1) = T(0+3,1+1) = T(3,2) = (5,7),
but T(0,1) + T(3,1) = (3,4) + (2,2) = (5,6), not (5,7).

6. T is bijective as it has an inverse Q(x,y) = ((x+y)/2,(y-x)/2).
Thanks from zylo
skipjack is offline  

  My Math Forum > College Math Forum > Abstract Algebra

discrete, discrete mathematics, group theory, linear transformation, mathematics, required, vector spaces

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Need Discrete mathematics help chris7789 Computer Science 0 September 11th, 2017 04:49 PM
Discrete Mathematics rntbeats Applied Math 3 November 23rd, 2014 02:38 AM
Discrete Mathematics. Shruthi318 Applied Math 0 November 9th, 2013 09:42 PM
discrete mathematics conradtsmith Abstract Algebra 1 April 19th, 2010 07:02 AM
discrete mathematics conradtsmith Number Theory 1 April 19th, 2010 06:11 AM

Copyright © 2019 My Math Forum. All rights reserved.