2. (5 points) Consider the transformation T: R² → R³ defined by T [2] = X 2x - Y 3x+4y (i) Show that T is a linear transformation by checking whether properties (a) and (b) hold. (a) T(u + v) = T(u) + T(v) for all u, v € R² (Additive Property) (b) T(ku) = kT(u) for all u € R² and k E R (Homogeneity Property) (ii) Show that T is a linear transformation, but this time write a short justifica- tion utilizing some theorems or facts that you know. Read your textbook.
2. (5 points) Consider the transformation T: R² → R³ defined by T [2] = X 2x - Y 3x+4y (i) Show that T is a linear transformation by checking whether properties (a) and (b) hold. (a) T(u + v) = T(u) + T(v) for all u, v € R² (Additive Property) (b) T(ku) = kT(u) for all u € R² and k E R (Homogeneity Property) (ii) Show that T is a linear transformation, but this time write a short justifica- tion utilizing some theorems or facts that you know. Read your textbook.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![2. (5 points) Consider the transformation T : R² → R³ defined by
-]
2x - Y
=
3x + 4y
T
X
Y
(i) Show that T is a linear transformation by checking whether properties (a)
and (b) hold.
(a) T(u+v) = T(u) +T(v) for all u, v € R² (Additive Property)
(b) T(ku) = kT(u) for all u € R² and k E R (Homogeneity Property)
(ii) Show that T is a linear transformation, but this time write a short justifica-
tion utilizing some theorems or facts that you know. Read your textbook.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fbec6f0-ea2c-44d4-90c4-3448f1ee2db9%2F7fbc2c35-4a88-4b9c-be6c-7c1025c95db8%2F9tcz46o_processed.png&w=3840&q=75)
Transcribed Image Text:2. (5 points) Consider the transformation T : R² → R³ defined by
-]
2x - Y
=
3x + 4y
T
X
Y
(i) Show that T is a linear transformation by checking whether properties (a)
and (b) hold.
(a) T(u+v) = T(u) +T(v) for all u, v € R² (Additive Property)
(b) T(ku) = kT(u) for all u € R² and k E R (Homogeneity Property)
(ii) Show that T is a linear transformation, but this time write a short justifica-
tion utilizing some theorems or facts that you know. Read your textbook.
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