Let ƒ : R² → R be defined by f((x, y)) = 4x − 6y +2. Is ƒ a linear transformation? = (1) f((x,y₁) + (x2,y₂)) = x₁ as x1, etc.) f((x1, y₁)) + f((x2, y₂)) = Does f((x1, y1) + (x2, y2)) = f((x₁, y₁)) + f((x2, y2)) for all (x1, y1), (x2, y2) € R²? • choose . Yes, they are equal . No, they are not equal (2) f(c(x,y)) = c(ƒ((x,y))) = — ( (3) Is f a linear transformation? choose (Enter + Does f(c(x,y)) = c(f((x,y))) for all c ER and all (x, y) = R²? • choose . Yes, they are equal . No, they are not equal f is a linear transformation • f is not a linear transformation
Let ƒ : R² → R be defined by f((x, y)) = 4x − 6y +2. Is ƒ a linear transformation? = (1) f((x,y₁) + (x2,y₂)) = x₁ as x1, etc.) f((x1, y₁)) + f((x2, y₂)) = Does f((x1, y1) + (x2, y2)) = f((x₁, y₁)) + f((x2, y2)) for all (x1, y1), (x2, y2) € R²? • choose . Yes, they are equal . No, they are not equal (2) f(c(x,y)) = c(ƒ((x,y))) = — ( (3) Is f a linear transformation? choose (Enter + Does f(c(x,y)) = c(f((x,y))) for all c ER and all (x, y) = R²? • choose . Yes, they are equal . No, they are not equal f is a linear transformation • f is not a linear transformation
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 4CM
Related questions
Question
Transcribed Image Text:Let ƒ : R² → R be defined by f((x, y)) = 4x − 6y +2. Is ƒ a
linear transformation?
=
(1) f((x,y₁) + (x2,y₂)) =
x₁ as x1, etc.)
f((x1, y₁)) + f((x2, y₂)) =
Does f((x1, y1) + (x2, y2)) = f((x₁, y₁)) + f((x2, y2))
for all (x1, y1), (x2, y2) € R²?
• choose
. Yes, they are equal
. No, they are not equal
(2) f(c(x,y)) =
c(ƒ((x,y))) = — (
(3) Is f a linear transformation?
choose
(Enter
+
Does f(c(x,y)) = c(f((x,y))) for all c ER and all
(x, y) = R²?
• choose
. Yes, they are equal
. No, they are not equal
f is a linear transformation
• f is not a linear transformation
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