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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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...
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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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