please write answer as a formula that returns a vector Let f : R → R³ be defined by f(x) = (8x, -7x, -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? chooseb. f(cx) ==c(f(x)) =Does f(cx) = c(f(x)) for all c, x ER? choosec. Is f a linear transformation? choose

Answered: Image /qna-images/answer/95f1505a-a0eb-4ecb-916b-62856b605284.jpg

Let f: R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = fƒ(x) + f(y) for all x, y < R? choose b. f(cz) = 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) = (8x, -7x, -9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = fƒ(x) + f(y) for all x, y < R? choose b. f(cz) = 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) = (8x, -7x, -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 ER? 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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