Exercise 10.1.1 Consider the following functions T: R³ → R². For each of these functions T, show that it is not linear either by showing that T does not preserve addition, or by showing that it does not preserve scalar multiplication, or by showing that it does not preserve the zero vector. (a) T (b) T (c) T Z X 3-4 = Z X Z x+2y+3z +1 2y-s = 2y+3x+z 1. sinx+2y+3z 2y+3x+z
Exercise 10.1.1 Consider the following functions T: R³ → R². For each of these functions T, show that it is not linear either by showing that T does not preserve addition, or by showing that it does not preserve scalar multiplication, or by showing that it does not preserve the zero vector. (a) T (b) T (c) T Z X 3-4 = Z X Z x+2y+3z +1 2y-s = 2y+3x+z 1. sinx+2y+3z 2y+3x+z
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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can you help me solve part b and c please?
![Exercise 10.1.1 Consider the following functions T: R³ → R². For each of these functions T, show that
it is not linear either by showing that T does not preserve addition, or by showing that it does not preserve
scalar multiplication, or by showing that it does not preserve the zero vector.
(a) T
(b) T
Z
X
[1]-
=
Z
X
1-
=
Z
(c) Ty
-2y+3z+1
2y-
?].
x+2y² +3z
2y+3x+z
sinx+2y+3z
2y+3x+z
].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52fb4760-8b56-41d1-811f-26cd2f9d5b41%2Fd2ddfcd3-8f9e-4768-9d72-e558b56db821%2Fys80y09_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 10.1.1 Consider the following functions T: R³ → R². For each of these functions T, show that
it is not linear either by showing that T does not preserve addition, or by showing that it does not preserve
scalar multiplication, or by showing that it does not preserve the zero vector.
(a) T
(b) T
Z
X
[1]-
=
Z
X
1-
=
Z
(c) Ty
-2y+3z+1
2y-
?].
x+2y² +3z
2y+3x+z
sinx+2y+3z
2y+3x+z
].
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