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Consider the transformation T: R³ R³ defined as (ED) - E T 3x-2y y+z-x 2 + 2y (a) Show that T is a linear transformation (you must show that all the requirements of the definition are satisfied). (b) Find the standard matrix A of T and show that the A is invertible and find its inverse. x (c) Show that TA-1 Ty 2 x x y for all ye R³. 2

Consider the transformation T: R³ R³ defined as (ED) - E T 3x-2y y+z-x 2 + 2y (a) Show that T is a linear transformation (you must show that all the requirements of the definition are satisfied). (b) Find the standard matrix A of T and show that the A is invertible and find its inverse. x (c) Show that TA-1 Ty 2 x x y for all ye R³. 2

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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Consider the transformation T: R3 R³ defined as (E)-[ 3x - 2y y+z-m z + 2y (a) Show that T is a linear transformation (you must show that all the requirements of the definition are satisfied). (b) Find the standard matrix A of T and show that the A is invertible and find its inverse. (B) - B (c) Show that TA-1 x for all y R³. 2
Transcribed Image Text:Consider the transformation T: R3 R³ defined as (E)-[ 3x - 2y y+z-m z + 2y (a) Show that T is a linear transformation (you must show that all the requirements of the definition are satisfied). (b) Find the standard matrix A of T and show that the A is invertible and find its inverse. (B) - B (c) Show that TA-1 x for all y R³. 2
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