A, BE R"Xn 2. Let n EN. Consider the following binary relation for A-B : 3Q E R"*": Q. A A= QB orthogonal Matrix (a) Show that ~ is an equivalence relation is

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...
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plz provide answer for part A

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)
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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