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Let f: R² → R be defined by f((x, y)) = -9x - 7y - 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 (x1, y₁), (x2, y2) € R²? choose 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) = R²? choose (Enter x₁ as x1, etc.) c. Is f a linear transformation? choose

Let f: R² → R be defined by f((x, y)) = -9x - 7y - 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 (x1, y₁), (x2, y2) € R²? choose 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) = R²? choose (Enter x₁ as x1, etc.) c. Is f a linear transformation? choose

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 4EQ
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Let f: R² → R be defined by f((x, y)) = −9x – 7y — 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 (x₁, y₁), (x2, 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 x₁ as x1, etc.)
Transcribed Image Text:Let f: R² → R be defined by f((x, y)) = −9x – 7y — 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 (x₁, y₁), (x2, 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 x₁ as x1, etc.)
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