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Let f: R² R be defined by f((x, y)) = 4x - 8y + 4. Is f 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 choose Yes, they are equal No, they are not equal b. f(c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f((x,y))) for all c ER and all (x, y) E R²? choose (Enter a₁ as x1, etc.). c. Is f a linear transformation? choose

Let f: R² R be defined by f((x, y)) = 4x - 8y + 4. Is f 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 choose Yes, they are equal No, they are not equal b. f(c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f((x,y))) for all c ER and all (x, y) E R²? choose (Enter a₁ as x1, etc.). c. Is f a linear transformation? choose

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f: R² → R be defined by f((x, y)) = 4x -8y +4. 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 (x₁, y₁), (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 E R and all (x, y) = R²? choose c. Is f a linear transformation? choose (Enter x₁ as x1, etc.) choose Yes, they are equal No, they are not equal
Transcribed Image Text:Let f: R² → R be defined by f((x, y)) = 4x -8y +4. 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 (x₁, y₁), (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 E R and all (x, y) = R²? choose c. Is f a linear transformation? choose (Enter x₁ as x1, etc.) choose Yes, they are equal No, they are not equal
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