→ R be defined by f((x, y)) = −4x – 2y. Is ƒ a linear transformation? Letf: R². a. f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x2, y2)) = = + Does f((x₁, y₁) + (x2, y2)) = f((x₁, y₁)) + ƒ((x2, y2)) for all (x1, y₁), (x2, Y2) E R²? choose . (Enter x₁ as x1, etc.) b. f(c(x, y)) = = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Is f a linear transformation? choose
→ R be defined by f((x, y)) = −4x – 2y. Is ƒ a linear transformation? Letf: R². a. f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x2, y2)) = = + Does f((x₁, y₁) + (x2, y2)) = f((x₁, y₁)) + ƒ((x2, y2)) for all (x1, y₁), (x2, Y2) E R²? choose . (Enter x₁ as x1, etc.) b. f(c(x, y)) = = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Is f a linear transformation? choose
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 27EQ
Related questions
Question
![→ R be defined by f((x, y)) = −4x – 2y. Is ƒ a linear transformation?
Letf: R².
a. f((x₁, y₁) + (x₂, y₂)) =
f((x₁, y₁)) + f((x2, y2)) =
=
+
Does f((x₁, y₁) + (x2, y2)) = f((x₁, y₁)) + ƒ((x2, y2)) for all (x1, y₁), (x2, Y2) E R²?
choose
. (Enter x₁ as x1, etc.)
b. f(c(x, y)) = =
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose
c. Is f a linear transformation? choose](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd29ed1ca-eabb-4fe1-ba2f-df7a36f73903%2F939134d7-b699-4bf6-82f7-65e028c74676%2F1wfso1r_processed.png&w=3840&q=75)
Transcribed Image Text:→ R be defined by f((x, y)) = −4x – 2y. Is ƒ a linear transformation?
Letf: R².
a. f((x₁, y₁) + (x₂, y₂)) =
f((x₁, y₁)) + f((x2, y2)) =
=
+
Does f((x₁, y₁) + (x2, y2)) = f((x₁, y₁)) + ƒ((x2, y2)) for all (x1, y₁), (x2, Y2) E R²?
choose
. (Enter x₁ as x1, etc.)
b. f(c(x, y)) = =
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose
c. Is f a linear transformation? choose
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