Let f: R → R³ be defined by f(x)a. f(x + y)b. f(cx) ==f(x) + f(y) =+Does f(x + y) = f(x) + f(y) for all x, y ER? choose==(7x, 7x, 2x). Is f a linear transformation?c(f(x))Does f(cx) = c(f(x)) for all c, x € R? choosec. Is f a linear transformation? choose

We have to check is linear transformation or not.

Let f: R → R³ be defined by f(x) = (7x, 7x, 2x). 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

Let f: R → R³ be defined by f(x) = (7x, 7x, 2x). 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

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

Let f: R → R³ be defined by f(x)
a. f(x + y)
b. f(cx) =
=
f(x) + f(y) =
+
Does f(x + y) = f(x) + f(y) for all x, y ER? choose
=
=
(7x, 7x, 2x). Is f a linear transformation?
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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