Let f: R → R³ be defined by f(x) = (-2x, 9x, 9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y = R? choose b. f(cx) = c(f(x)) = = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
Let f: R → R³ be defined by f(x) = (-2x, 9x, 9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y = R? choose b. f(cx) = c(f(x)) = = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 4CM
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Question
![Let ƒ : R → R³ be defined by f(x) = (-2x, 9x, 9x). Is ƒ a linear transformation?
a. f(x + y) =
f(x) + f(y) =
+
Does f(x + y) = f(x) + f(y) for all x, y = R? choose
b. f(cx)
=
c(f(x))
Does f(cx) = c(f(x)) for all c, x = R? choose
c. Is f a linear transformation? choose](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d39a54-7451-4975-bf07-83fb2d3bea67%2Fbe0e091f-71b6-4940-8988-f3a871e26614%2F26eqhwf_processed.png&w=3840&q=75)
Transcribed Image Text:Let ƒ : R → R³ be defined by f(x) = (-2x, 9x, 9x). Is ƒ a linear transformation?
a. f(x + y) =
f(x) + f(y) =
+
Does f(x + y) = f(x) + f(y) for all x, y = R? choose
b. f(cx)
=
c(f(x))
Does f(cx) = c(f(x)) for all c, x = R? choose
c. Is f a linear transformation? choose
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