Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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 ER? 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) = (x, 6x², 3x). 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 ER? 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 16CM

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Question

please write answer as a formula that returns a vector

Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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