4. Let T: R4 → R³ with T 0-1 = a. What is the domain of T'? C. b. What is the codomain of T'? x + 2y + z -3x - 2y + 3w 4y + 3z + 3w 1 H 5 2 What is the image of under T'? 2 d. Find all the vectors that T maps to -1 H 5 Is T one-to-one? Justify your answer. f. Is Tonto? Justify your answer. g. Describe the kernel of T. Give a basis for it. h. Describe the range of T. Give a basis for it.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Question
4. Let T: R4
a.
C.
R³ with T
e.
(ED-L
b. What is the codomain of T'?
f.
What is the domain of T'?
1
H
2
x + 2y + z
-3x - 2y + 3w
4y + 3z + 3w
What is the image of
d. Find all the vectors that T maps to
under T'?
5
Is T one-to-one? Justify your answer.
Is Tonto? Justify your answer.
g. Describe the kernel of T. Give a basis for it.
h. Describe the range of T. Give a basis for it.
Transcribed Image Text:4. Let T: R4 a. C. R³ with T e. (ED-L b. What is the codomain of T'? f. What is the domain of T'? 1 H 2 x + 2y + z -3x - 2y + 3w 4y + 3z + 3w What is the image of d. Find all the vectors that T maps to under T'? 5 Is T one-to-one? Justify your answer. Is Tonto? Justify your answer. g. Describe the kernel of T. Give a basis for it. h. Describe the range of T. Give a basis for it.
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