Tell whether the multiplicative group of nonsingular upper triangular matrices, that is, matrices like a b 0 d where the determinant ad is nonzero, is a normal subgroup of the group GL(2,R) of all nonsingular 2x2 matrices over the real numbers under the operation of multiplication. One way to do this is to take the particular matrix 0 1 1 0

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.8: Solving Systems With Cramer's Rule
Problem 3SE: Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
Question

Tell whether the multiplicative group of nonsingular upper triangular matrices, that is, matrices like

a b

0 d

where the determinant ad is nonzero, is a normal subgroup of the group GL(2,R) of all nonsingular 2x2 matrices over the real numbers under the operation of multiplication. One way to do this is to take the particular matrix

0 1

1 0

and conjugate the matrix in the previous display by this matrix and see if the form is preserved.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Groups
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning