2 Let f : R ² → R be defined by f((x, y)) = 6y – 9x. Is f a linear transformation? a. f ((x₁, y₁ ) + (x2, y₂)) = 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 ) E R ²? 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) =R ²? choose c. Is f a linear transformation? choose . (Enter x₁ as x1,

2 Let f : R ² → R be defined by f((x, y)) = 6y – 9x. Is f a linear transformation? a. f ((x₁, y₁ ) + (x2, y₂)) = 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 ) E R ²? 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) =R ²? choose c. Is f a linear transformation? choose . (Enter x₁ as x1,

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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