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 X y 7 X (b) T y Z (c) T x+2y+3z +1 2y-3x+z x+2y² +3z 2y+3x+z 8-1 y 7 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 X y 7 X (b) T y Z (c) T x+2y+3z +1 2y-3x+z x+2y² +3z 2y+3x+z 8-1 y 7 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 please solve (c) ?
![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.
X
¹8-
y
Z
(a) T
(b) T
(c) T
X
y
Z
=
x+2y+3z +1
2y - 3x+z
x+2y² +3z
2y+3x+z
X
11-0
y
Z
]
sinx+2y+3z
2y+3x+z
]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98a85d3f-1221-4cd9-b5c2-c225eed9a46f%2F8d54f19c-e217-4866-b036-f3d933bdfc4b%2Fdp6kw9_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.
X
¹8-
y
Z
(a) T
(b) T
(c) T
X
y
Z
=
x+2y+3z +1
2y - 3x+z
x+2y² +3z
2y+3x+z
X
11-0
y
Z
]
sinx+2y+3z
2y+3x+z
]
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