Exercise 10.1.2 Consider the following functions T: R³ → R2. For each function T, show that T is a linear transformation. Do this by showing that T is a matrix transformation, i.e., find a matrix A such that T(v) = Av. (a) T (b) T (c) T Z X Z X y Z (d) T y 1 1 = 2y-3x+z 7x+2y+z 3x - 11y+2z 3x+2y+z x+2y+6z 2y-5x+z x+y+z
Exercise 10.1.2 Consider the following functions T: R³ → R2. For each function T, show that T is a linear transformation. Do this by showing that T is a matrix transformation, i.e., find a matrix A such that T(v) = Av. (a) T (b) T (c) T Z X Z X y Z (d) T y 1 1 = 2y-3x+z 7x+2y+z 3x - 11y+2z 3x+2y+z x+2y+6z 2y-5x+z x+y+z
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 54EQ
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can you please solve (c) & (d) ?
![Exercise 10.1.2 Consider the following functions T: R³ → R². For each function T, show that I is a
linear transformation. Do this by showing that T is a matrix transformation, i.e., find a matrix A such that
T(v) = Av.
(a) T
(b) T
(c) T
(d) T
X
y
X
B
Z
y =
X
y
Z
X
=
Z
x+2y+3z
2y-3x+z
7x+2y+z
3x - 11y+2z
2y-5x+z
[:]-[***]
y =
x+y+z
3x+2y+z
x+2y+6z](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98a85d3f-1221-4cd9-b5c2-c225eed9a46f%2F86959c89-c8d8-4ab9-8833-e34a76af7eba%2Funoyt89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 10.1.2 Consider the following functions T: R³ → R². For each function T, show that I is a
linear transformation. Do this by showing that T is a matrix transformation, i.e., find a matrix A such that
T(v) = Av.
(a) T
(b) T
(c) T
(d) T
X
y
X
B
Z
y =
X
y
Z
X
=
Z
x+2y+3z
2y-3x+z
7x+2y+z
3x - 11y+2z
2y-5x+z
[:]-[***]
y =
x+y+z
3x+2y+z
x+2y+6z
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