() The operation of subtraction A, BHA-B of matrices A, Bhaving the same size is defined by as follows: if A = |||| and B = ||by||,then A-B= ||aij – by|l- For instance, G :)-(: ) - (1–4 2-3) 3-2 4-1, Like other matrix operations, the operation of subtraction is very helpful when dealing with relations: it often enables one to get a clearer picture, to make surer conclusions, to avoid mistakes, etc. One of the possible applications is as follows. Let S,T be relations on a finite set A and let Ms and My be the matrices of S and T, respectively. Then the number of negative entries of the matrix M7 - Ms is equal to the cardinality of the set . (please enter an appropriate expression involving the sets S and T; use the keywords union, intersection, and setminus for the set-theoretic operations n, U, and \, respectively, if necessary) In particular, all entries of the matrix MT – Ms are nonnegative if and only if the relation S is . (enter a correct word) in the relation T. (i) Consider the relation R= {(1,1), (1,3), (1, 4), (1,5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3,1), (3, 3), (3, 4), (3,5), (4, 1), (4, 3), (4, 4), (4, 5), (5, 5)} on the set A = {1,2, 3, 4, 5}. Verify whether or not the relation Ris transitive by realizing the following plan. (a) Find the matrix MRof the relation R (here, and below in (b,c), please enter the matrix row-by-row in the five input fields below; when entering each row, separate the entries by single spaces):
() The operation of subtraction A, BHA-B of matrices A, Bhaving the same size is defined by as follows: if A = |||| and B = ||by||,then A-B= ||aij – by|l- For instance, G :)-(: ) - (1–4 2-3) 3-2 4-1, Like other matrix operations, the operation of subtraction is very helpful when dealing with relations: it often enables one to get a clearer picture, to make surer conclusions, to avoid mistakes, etc. One of the possible applications is as follows. Let S,T be relations on a finite set A and let Ms and My be the matrices of S and T, respectively. Then the number of negative entries of the matrix M7 - Ms is equal to the cardinality of the set . (please enter an appropriate expression involving the sets S and T; use the keywords union, intersection, and setminus for the set-theoretic operations n, U, and \, respectively, if necessary) In particular, all entries of the matrix MT – Ms are nonnegative if and only if the relation S is . (enter a correct word) in the relation T. (i) Consider the relation R= {(1,1), (1,3), (1, 4), (1,5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3,1), (3, 3), (3, 4), (3,5), (4, 1), (4, 3), (4, 4), (4, 5), (5, 5)} on the set A = {1,2, 3, 4, 5}. Verify whether or not the relation Ris transitive by realizing the following plan. (a) Find the matrix MRof the relation R (here, and below in (b,c), please enter the matrix row-by-row in the five input fields below; when entering each row, separate the entries by single spaces):
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Discrete Mathematics

Transcribed Image Text:) The operation of subtraction
А, ВНА-В
of matrices A, Bhaving the same size is defined by as follows: if A = ||aij|| and B = ||b|l, then
A - B= ||aj – bij|l-
For instance,
(: )-(: )-()-(G :)
(1-4 2-3
3 –2 4-1
3
Like other matrix operations, the operation of subtraction is very helpful when dealing with relations: it often enables one to get a clearer picture, to make surer
conclusions, to avoid mistakes, etc. One of the possible applications is as follows.
Let S, T be relations on a finite set A and let Ms and MT be the matrices of S and T, respectively. Then the number of negative entries of the matrix
Mr - Ms
is equal to the cardinality of the set. (please enter an appropriate expression involving the sets S and T; use the keywords union, intersection, and setminus
for the set-theoretic operations n, U, and \, respectively, if necessary)
In particular, all entries of the matrix MT – Ms are nonnegative if and only if the relation S is . (enter a correct word)
in the relation T.
(ii) Consider the relation
R= {(1,1), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),
(3,1), (3, 3), (3, 4), (3, 5), (4, 1), (4, 3), (4, 4), (4, 5), (5, 5)}
on the set A = {1,2, 3, 4, 5}. Verify whether or not the relation Ris transitive by realizing the following plan.
(a) Find the matrix MR of the relation R (here, and below in (b,c), please enter the matrix row-by-row in the five input fields below; when entering each row, separate the
entries by single spaces):

Transcribed Image Text:(b) Find the matrix M2 of the relation R2:
(c) Now find-for your own use-the matrix
MR- Me.
This matrix has . (please enter a suitable number)
negative entries, which means that, |R \R =
%3D
(d) Accordingly, by (1) and by (c), the relation R . (enter two correct words, or three correct words)
in the relation R, and hence the relation R
is
whie one i choose
O is not
transitive.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

