Let f: R² → R be defined by f((x, y)) = 9y-7x. 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> ER²? choose b. f(c(x, y)) = . (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) ER²? choose c. Is f a linear transformation? choose

Let f: R² → R be defined by f((x, y)) = 9y-7x. 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> ER²? choose b. f(c(x, y)) = . (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) ER²? choose c. Is f a linear transformation? choose

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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