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
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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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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