Consider the transformation T : R3 → R3 defined as (matrix is attached) 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. c) Is attached in image

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the transformation T : R3 → R3 defined as (matrix is attached)

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.

c) Is attached in image

(c) Show that TA-1
(-) -
Ty
X
Xx
y for all y € R³.
Transcribed Image Text:(c) Show that TA-1 (-) - Ty X Xx y for all y € R³.
T
(1)
Зу - 2z
z+ x - y
x + 2z
Transcribed Image Text:T (1) Зу - 2z z+ x - y x + 2z
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