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Let SL(n, R) denote the collection of n x n matrices whose determinant is equal to 1. Prove that SL(n, R) is a subgroup of GL(n, R). (It is called the special linear group.) 2. Let H denote the subset of GL(2, R) consisting of elements of GL(2, R) whose four entries are all rational numbers. Prove that H is a subgroup of GL(2, R).

Let SL(n, R) denote the collection of n x n matrices whose determinant is equal to 1. Prove that SL(n, R) is a subgroup of GL(n, R). (It is called the special linear group.) 2. Let H denote the subset of GL(2, R) consisting of elements of GL(2, R) whose four entries are all rational numbers. Prove that H is a subgroup of GL(2, R).

Advanced Engineering Mathematics
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 SL(n, R) denote the collection of n × n matrices whose determinant is equal to 1. Prove that SL(n, R) is a subgroup of GL(n, R). (It is called the special linear group.) 2. Let H denote the subset of GL(2, R) consisting of elements of GL(2, R) whose four entries are all rational numbers. Prove that H is a subgroup of GL(2, R).
Transcribed Image Text:Let SL(n, R) denote the collection of n × n matrices whose determinant is equal to 1. Prove that SL(n, R) is a subgroup of GL(n, R). (It is called the special linear group.) 2. Let H denote the subset of GL(2, R) consisting of elements of GL(2, R) whose four entries are all rational numbers. Prove that H is a subgroup of GL(2, R).
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