Let M2(R) be the set of 2 x 2 matrices with real entrics. That is: a b M2(R) = c d • ([: :)) (l: Recall that the Determinant of a matrix is det a b = ad - bc. Define the following relation c d on M2(R): R = {(A, B) E M2(R) × M2(R) | det4 A) < det(B)}. 1 2 1. Find 3 distinct clements in the class 43 2. Prove that R is an Reflexive and Transitive and not Symmetric.

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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Let M2(R) be the set of 2 x 2 matrices with real entries. That is:
M2(R) = { A = la, b, c, d e R.
([::)
Recall that the Determinant of a matrix is det
a b
ad- bc. Define the following relation
c d
on M2(R):
R = {(A, B) e M2(R) x M2(R) | det4A) < det(B)}-
1
1 2
1. Find 3 distinct clements in the class
4 3
R
2. Prove that R is an Rellexive and Transitive and not Symmetric.
Transcribed Image Text:Let M2(R) be the set of 2 x 2 matrices with real entries. That is: M2(R) = { A = la, b, c, d e R. ([::) Recall that the Determinant of a matrix is det a b ad- bc. Define the following relation c d on M2(R): R = {(A, B) e M2(R) x M2(R) | det4A) < det(B)}- 1 1 2 1. Find 3 distinct clements in the class 4 3 R 2. Prove that R is an Rellexive and Transitive and not Symmetric.
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