Let f:R→R be defined by f(x)=8x. Is f a linear transformation?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 8EQ: In Exercises 1-12, determine whether T is a linear transformation. 8. defined by
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Let f:R→R be defined by f(x)=8x. Is f a linear transformation?

a. f(x + y) =
%3D
f(x) + f(y) =
Does f(x + y) = f(x)+ f(y) for all x, y E R? choose
b. f(cx) =
c(f(x)) =
Does f(cx) = c(f(x)) for all c, x E R? choose
c. Is f a linear transformation? choose
Transcribed Image Text:a. f(x + y) = %3D f(x) + f(y) = Does f(x + y) = f(x)+ f(y) for all x, y E R? choose b. f(cx) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose c. Is f a linear transformation? choose
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