### Question: Group Theory in Linear AlgebraThe group $ SL(2, \mathbb{R}) $ of 2 by 2 matrices with determinant 1 is a normal subgroup of $ GL(2, \mathbb{R}) $, the group of 2 by 2 matrices with nonzero determinant. True or false?- [ ] True- [ ] FalseThis question tests knowledge of group theory concepts, specifically involving special linear groups and general linear groups. Normal subgroups play a key role in understanding group structures and quotient groups.

Answered: The group SL (2, R) of 2 by 2 matrices…

The group SL (2, R) of 2 by 2 matrices with determinant 1 is a normal subgroup of GL (2, R), the group of 2 by 2 matrices with nonzero determinant. True of false?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 11E: Find all homomorphic images of the quaternion group.

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