A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal Matrix (a) Show that ~ is an equivalence relation is A € GL(n, R) A A B BEGL(n, R) A (A-1)"- (B-')" (b) Show:
A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal Matrix (a) Show that ~ is an equivalence relation is A € GL(n, R) A A B BEGL(n, R) A (A-1)"- (B-')" (b) Show:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
ques2
plz provide answer for part b
![A, B E RXn
2. Let n EN. Consider the following binary relation for
A~ B : 3Q E R"Xn: Q.
A A= QB
orthogonal Matrix
Rxn
is
(a) Show that ~ is an equivalence relation
A E GL(n, R) A A~B = B€ GL(n, R) A (A-1)T ~~ (B-1)T
(b) Show:
= Q, ~ Q2
(c) Show: 1. Q2 € Raxn,
orthogonal matrices
A~B Σ-Σ
(d) Show:
ij=1
ij=1
%3B
A = (a,)ij=1, und B =
there is
(Note: track ATA)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e5b1a56-3032-449a-acc6-d2196fb84e38%2F70c31223-ccdd-4c30-8bd7-fd19c10f2d45%2F9jtt4yq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A, B E RXn
2. Let n EN. Consider the following binary relation for
A~ B : 3Q E R"Xn: Q.
A A= QB
orthogonal Matrix
Rxn
is
(a) Show that ~ is an equivalence relation
A E GL(n, R) A A~B = B€ GL(n, R) A (A-1)T ~~ (B-1)T
(b) Show:
= Q, ~ Q2
(c) Show: 1. Q2 € Raxn,
orthogonal matrices
A~B Σ-Σ
(d) Show:
ij=1
ij=1
%3B
A = (a,)ij=1, und B =
there is
(Note: track ATA)
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