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Let f: R² → R be defined by f((x, y)) = 8x +9y. 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) E 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 ₁ as x1, etc.)

Let f: R² → R be defined by f((x, y)) = 8x +9y. 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) E 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 ₁ as x1, etc.)

Elementary Linear Algebra (MindTap Course List)
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 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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Let f: R² → R be defined by f((x, y)) = 8x +9y. Is f a linear transformation? a. f((x1, y₁) + (x2, Y₂)) = f((x1, y₁)) + f((x2, Y2)) = + Does f((x1, y₁) + (x2, Y₂)) = ƒ((X₁,Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, Y2) € R²? choose E 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 ₁ as x1, etc.)
Transcribed Image Text:Let f: R² → R be defined by f((x, y)) = 8x +9y. Is f a linear transformation? a. f((x1, y₁) + (x2, Y₂)) = f((x1, y₁)) + f((x2, Y2)) = + Does f((x1, y₁) + (x2, Y₂)) = ƒ((X₁,Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, Y2) € R²? choose E 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 ₁ as x1, etc.)
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