Let ƒ : R → R³ be defined by f(x) = (x, −3x², −9x). Is ƒ a linear transformation? a. f(x + y) = ƒ(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(ƒ(x)) for all c, x ¤ R? choose c. Is f a linear transformation? choose

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
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Let ƒ : R → R³ be defined by ƒ(x) = (x, −3x², −9x). Is ƒ a linear transformation?
a. f(x + y) =
=
f(x) + f(y)
+
Does f(x + y) = ƒ(x) + f(y) for all x, y E 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
Transcribed Image Text:Let ƒ : R → R³ be defined by ƒ(x) = (x, −3x², −9x). Is ƒ a linear transformation? a. f(x + y) = = f(x) + f(y) + Does f(x + y) = ƒ(x) + f(y) for all x, y E 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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