Let f: R² → R be defined by f((x, y)) = 6x- -9y - 9. Is f a linear transformation? a. f((x1, y₁) + (x2, y2)) = f((x1, y₁)) + f((x2, y2)) = + Does f((x1, y₁) + (x2, Y₂)) = f((x₁, Y₁)) + f((x2, y₂)) for all (₁, ₁), (2, Y2) € R²? choose b. f(c(x, y)) = = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose c. Is f a linear transformation? choose . (Enter ₁ as x1, etc.) <
Let f: R² → R be defined by f((x, y)) = 6x- -9y - 9. Is f a linear transformation? a. f((x1, y₁) + (x2, y2)) = f((x1, y₁)) + f((x2, y2)) = + Does f((x1, y₁) + (x2, Y₂)) = f((x₁, Y₁)) + f((x2, y₂)) for all (₁, ₁), (2, Y2) € R²? choose b. f(c(x, y)) = = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose c. Is f a linear transformation? choose . (Enter ₁ as x1, etc.) <
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
Related questions
Question
![Let f: R² → R be defined by f((x, y)) = 6x - 9y - 9. Is ƒ a linear transformation?
a. f((x1, y₁) + (x2, y₂)) =
f((x1, y₁)) + f((x2, Y2)) =
+
Does f((1, ₁) + (x2, Y₂)) = f((x₁, Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, 2) € R²? choose
b. f(c(x, y))
=
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose
c. Is f a linear transformation? choose
(Enter ₁ as x1, etc.)
<](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b4d98a6-2ed4-451a-82b3-b3630dcf9fce%2F5f53272b-08b5-4bf8-9f13-913f066dbcda%2Fg59h4dp_processed.png&w=3840&q=75)
Transcribed Image Text:Let f: R² → R be defined by f((x, y)) = 6x - 9y - 9. Is ƒ a linear transformation?
a. f((x1, y₁) + (x2, y₂)) =
f((x1, y₁)) + f((x2, Y2)) =
+
Does f((1, ₁) + (x2, Y₂)) = f((x₁, Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, 2) € R²? choose
b. f(c(x, y))
=
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose
c. Is f a linear transformation? choose
(Enter ₁ as x1, etc.)
<
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