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1. In this problem, you will need to know that the determinant function is a function from {n x n matrices} → R, a matrix is invertible exactly when its determinant is nonzero, and for all n x n matrices A and B, det(AB) det (A) det(B). If we denote the set of invertible n x n matrices as GL(n, R), then the determinant gives a function from GL(n, R) to 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.)

1. In this problem, you will need to know that the determinant function is a function from {n x n matrices} → R, a matrix is invertible exactly when its determinant is nonzero, and for all n x n matrices A and B, det(AB) det (A) det(B). If we denote the set of invertible n x n matrices as GL(n, R), then the determinant gives a function from GL(n, R) to 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.)

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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1. In this problem, you will need to know that the determinant function is a function from {n x n matrices} → R, a matrix is invertible exactly when its determinant is nonzero, and for all n x n matrices A and B, det(AB) det (A) det (B). If we denote the set of invertible n x n matrices as GL(n, R), then the determinant gives a function from GL(n, R) to 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.)
Transcribed Image Text:1. In this problem, you will need to know that the determinant function is a function from {n x n matrices} → R, a matrix is invertible exactly when its determinant is nonzero, and for all n x n matrices A and B, det(AB) det (A) det (B). If we denote the set of invertible n x n matrices as GL(n, R), then the determinant gives a function from GL(n, R) to 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.)
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