Prove that the zero transformation and the identity transformation are linear transformations. (a) the zero transformation Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V → W be the zero transformation. Which of the following proves the zero transform linear transformation? (Select all that apply.) O T(c + v) = c + 0 = c + T(v) O T(vw) = 0 = 0.0 = T(v) T(w) O T(cvw) = 0 = co · 0 = cT(v) T(w) O T(cv) = 0 = c0 = cT(v) O CT(v + w) = c(0 + 0) = cT(v) + cT(w) O T(v + w) = 0 = 0 +0 = T(v) + T(w) (b) the identity transformation Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V→ V be the identity transformation. Which of the following proves the identity transform linear transformation? (Select all that apply.) O T(cv) = cV = cT(v) O T(vw) = vw = T(v) T(w) O CT(v + w) = c(v + w) = cT(v) + cT(w) T(v + w) = v + w = T(v) + T(w) O T(c + v) = c + v = c + T(v) T(cvw) = cvw = cT(v) T(w)
Prove that the zero transformation and the identity transformation are linear transformations. (a) the zero transformation Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V → W be the zero transformation. Which of the following proves the zero transform linear transformation? (Select all that apply.) O T(c + v) = c + 0 = c + T(v) O T(vw) = 0 = 0.0 = T(v) T(w) O T(cvw) = 0 = co · 0 = cT(v) T(w) O T(cv) = 0 = c0 = cT(v) O CT(v + w) = c(0 + 0) = cT(v) + cT(w) O T(v + w) = 0 = 0 +0 = T(v) + T(w) (b) the identity transformation Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V→ V be the identity transformation. Which of the following proves the identity transform linear transformation? (Select all that apply.) O T(cv) = cV = cT(v) O T(vw) = vw = T(v) T(w) O CT(v + w) = c(v + w) = cT(v) + cT(w) T(v + w) = v + w = T(v) + T(w) O T(c + v) = c + v = c + T(v) T(cvw) = cvw = cT(v) T(w)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![Prove that the zero transformation and the identity transformation are linear transformations.
(a) the zero transformation
Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V→ W be the zero transformation. Which of the following proves the zero transform
linear transformation? (Select all that apply.)
Т(с + v) 3D с +0 %3D с + T(v)
=
T(vw)
= 0
= 0 : 0
T(v) T(w)
T(cvw) = 0 = c0 ·
0 = cT(v) T(w)
%3D
T(cv)
= 0 = c0 = cT(v)
CT(v + w) = c(0 + 0) = cT(v) + cT(w)
%3D
T(v + w) = 0 = 0 + 0 =
T(v) + T(w)
(b) the identity transformation
Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V → V be the identity transformation. Which of the following proves the identity transform
linear transformation? (Select all that apply.)
T(cv) = cv =
cT(v)
T(vw)
= VW =
T(v) T(w)
CT(v + w)
c(v + w)
CT(v) + cT(w)
T(v + w) = v + w = T(v) + T(w)
T(c + v) = c + v = c + T(v)
T(cvw)
= CVw =
CT(v) T(w)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe50f82ed-b28c-4fce-a220-85939dc49aaf%2Fe32a4536-09e6-4081-8e73-218c3372b05f%2Fabotsr_processed.png&w=3840&q=75)
Transcribed Image Text:Prove that the zero transformation and the identity transformation are linear transformations.
(a) the zero transformation
Let V and W be vector spaces, let v and w be vectors in V, let c be a scalar, and let T: V→ W be the zero transformation. Which of the following proves the zero transform
linear transformation? (Select all that apply.)
Т(с + v) 3D с +0 %3D с + T(v)
=
T(vw)
= 0
= 0 : 0
T(v) T(w)
T(cvw) = 0 = c0 ·
0 = cT(v) T(w)
%3D
T(cv)
= 0 = c0 = cT(v)
CT(v + w) = c(0 + 0) = cT(v) + cT(w)
%3D
T(v + w) = 0 = 0 + 0 =
T(v) + T(w)
(b) the identity transformation
Let V be a vector space, let v and w be vectors in V, let c be a scalar, and let T: V → V be the identity transformation. Which of the following proves the identity transform
linear transformation? (Select all that apply.)
T(cv) = cv =
cT(v)
T(vw)
= VW =
T(v) T(w)
CT(v + w)
c(v + w)
CT(v) + cT(w)
T(v + w) = v + w = T(v) + T(w)
T(c + v) = c + v = c + T(v)
T(cvw)
= CVw =
CT(v) T(w)
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