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Let f : R → R³ be defined by f(x) = (5x, –5x, 5x). Is ƒ a linear transformation? a. f(x + y) f(x) + f(y) = Does f(x + y) = f(x)+ f(y) for all x, y E R? choose b. f(cæ) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose c. Is fa linear transformation? choose

Let f : R → R³ be defined by f(x) = (5x, –5x, 5x). Is ƒ a linear transformation? a. f(x + y) f(x) + f(y) = Does f(x + y) = f(x)+ f(y) for all x, y E R? choose b. f(cæ) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x E R? choose c. Is fa linear transformation? choose

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 12EQ
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Let f : R → R³ be defined by f(x) = (5x, –5x, 5x). Is f a linear transformation? a. f(x + y) 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 %3D c. Is f a linear transformation? choose
Transcribed Image Text:Let f : R → R³ be defined by f(x) = (5x, –5x, 5x). Is f a linear transformation? a. f(x + y) 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 %3D c. Is f a linear transformation? choose
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