menu
Login
Register
search
Log In
account_circle
Log In
Email or Username
Password
Remember
Log In
Register
I forgot my password
Register
Username
Email
Password
Register
add
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Barc Interview Experience 2020- CSE stream
JEST 2021 registrations are open
TIFR GS-2021 Online Application portal
IIT Jodhpur Mtech AI - Interview Expierence (Summer Admission)
Interview experience at IIT Tirupati for MS program winter admission
Subjects
All categories
General Aptitude
(2.1k)
Engineering Mathematics
(8.5k)
Discrete Mathematics
(6k)
Mathematical Logic
(2.1k)
Set Theory & Algebra
(1.6k)
Combinatory
(1.4k)
Graph Theory
(885)
Probability
(1.1k)
Linear Algebra
(783)
Calculus
(645)
Digital Logic
(3k)
Programming and DS
(5.1k)
Algorithms
(4.5k)
Theory of Computation
(6.3k)
Compiler Design
(2.2k)
Operating System
(4.7k)
Databases
(4.3k)
CO and Architecture
(3.5k)
Computer Networks
(4.3k)
Non GATE
(1.2k)
Others
(1.3k)
Admissions
(595)
Exam Queries
(838)
Tier 1 Placement Questions
(16)
Job Queries
(71)
Projects
(19)
Unknown Category
(1.1k)
Recent Blog Comments
Yep, the problem was the theme π . I can see...
@Ayush I think problem is because of dark theme,...
then only someone from the officials can help...
Nope, it doesn't. I have tried everything.
hover mouse over "Taken " (or anywhere in that...
Network Sites
GO Mechanical
GO Electrical
GO Electronics
GO Civil
CSE Doubts
#set theory #groups
2
votes
205
views
Consider the set H of all 3 Γ 3 matrices of the type:
$\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$
where a, b, c, d, e and f are real numbers and $abc β 0$. Under the matrix multiplication operation, the set H is:
(a) a group
(b) a monoid but not a group
(c) a semigroup but not a monoid
(d) neither a group nor a semigroup
set-theory&algebra
group-theory
matrices
asked
Jan 5, 2019
in
Set Theory & Algebra
Kunal Kadian
edited
Jan 5, 2019
by
Kunal Kadian
205
views
answer
comment
0
option b ?
0
Answer given is C. You can anyways explain your choice of option.
0
Monoid means there is an identity element which in this case should be identity matrix. So I think it should be a Monoid
2
It should be a group.
As the inverse of an upper triangular matrix is always upper triangular and exists when all diagonals are non zero.
Please
log in
or
register
to add a comment.
Please
log in
or
register
to answer this question.
2
Answers
0
votes
Answer (a). This is a group. This satisfies closure and associativity properties.
Identity element is the 3x3 Identity matrix. The inverse also exists because the determinant, a*b*c, is non-zero.
It satisfies all the properties of a group. Hence, it is a group
answered
Nov 29, 2019
GoalSet1
comment
Please
log in
or
register
to add a comment.
0
votes
Answer is (a). Group.
Matrix operation multiplication and addition satisfies closure, associative, identity ($I_{3}$ ).
For addition inverse will always exist. (Null Matrix).
For Multiplication for singular matrix inverse mayn't exist. But here there is a condition that diagonal element product is non zero. Due to this restriction it will be non singular.
answered
Dec 3, 2019
smsubham
comment
Please
log in
or
register
to add a comment.
β Prev.
Next β
β Prev. Qn. in Sub.
Next Qn. in Sub. β
Related questions
0
votes
1
answer
1
213
views
Made Easy Test Series 2019: Set theory & Algebra - Groups
set of all possible diagonal matrix of order n ans given monoid my doubt-why it cannot have inverse??
set of all possible diagonal matrix of order n ans given monoid my doubt-why it cannot have inverse??
asked
Jan 24, 2019
in
Set Theory & Algebra
priyanka manwani
213
views
discrete-mathematics
set-theory&algebra
group-theory
madeeasy-testseries-2019
made-easy-test-series
0
votes
1
answer
2
135
views
Zeal Test Series 2019: Set Theory & Algebra - Groups
asked
Dec 22, 2018
in
Set Theory & Algebra
Prince Sindhiya
135
views
discrete-mathematics
set-theory&algebra
group-theory
zeal
zeal2019
0
votes
0
answers
3
109
views
Virtual Gate Test Series: Discrete Mathematics - Set Theory & Algebra - Groups
asked
Oct 15, 2018
in
Set Theory & Algebra
Prince Sindhiya
109
views
discrete-mathematics
set-theory&algebra
group-theory
virtual-gate-test-series
0
votes
0
answers
4
73
views
Zeal Workbook: Set Theory & Algebra - Groups
$\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$
$\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$
asked
Aug 22, 2018
in
Set Theory & Algebra
Prince Sindhiya
73
views
discrete-mathematics
set-theory&algebra
group-theory
zeal
zeal-workbook
...