Letf: R → R³ be defined by f(x) = (2x, 4x, -5x). Isf a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y ER? choose b. f(cx) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x ER? 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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Letf: RR3³ be defined by f(x) = (2x, 4x, -5x). Isf a linear transformation?
a. f(x + y) =
f(x) + f(y) =
+
Does f(x + y) = f(x) + f(y) for all x,y ER? choose
b. f(cx) =
c(f(x)) =
Does f(cx) = c(f(x)) for all c, x E R? choose
c. Is f a linear transformation? choose
Transcribed Image Text:Letf: RR3³ be defined by f(x) = (2x, 4x, -5x). Isf a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x,y ER? choose b. f(cx) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose c. Is f a linear transformation? choose
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