Let T: Rm → R" and S: RRP be linear transformations. Then So T: RRP is a linear transformation. Moreover, their standard matrices are related by [So T] = [S][T]. Verify the result of the theorem above for the following S and T by finding the matrix of S o 7 by direct substitution and by matrix multiplication of [S][T]. 8-22-2-43 X3 (a) by direct substitution (b) by matrix multiplication

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
icon
Related questions
Question
Let T: Rm → R" and S: RRP be linear transformations. Then So T: RRP is a linear transformation. Moreover, their standard matrices are related by
[So T] = [S][T].
Verify the result of the theorem above for the following S and T by finding the matrix of S o 7 by direct substitution and by matrix multiplication of [S][T].
8-22-2-43
X3
(a) by direct substitution
(b) by matrix multiplication
Transcribed Image Text:Let T: Rm → R" and S: RRP be linear transformations. Then So T: RRP is a linear transformation. Moreover, their standard matrices are related by [So T] = [S][T]. Verify the result of the theorem above for the following S and T by finding the matrix of S o 7 by direct substitution and by matrix multiplication of [S][T]. 8-22-2-43 X3 (a) by direct substitution (b) by matrix multiplication
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
steps

Unlock instant AI solutions

Tap the button
to generate a solution

Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax