a. f(x + y) = -5x-5y, 6x+6y, 5x+5y f(x) + f(y) = -5x, 6x, 5x + -5y,6y, 5y Does f(x + y) = f(x) + f(y) for all x, y ER? Yes, they are equal b. f(cx) = -5cx, 6cx, 5cx c(f(x)) = C -5x, 6x, 5x Does f(cx) = c(f(x)) for all c, x E R? Yes, they are equal c. Isf a linear transformation? f is a linear transformation

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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]Let ƒ : R → R³ be defined by f(x) = (−5x, 6x, 5x). Is ƒ a linear transformation?
a. f(x + y) = -5x-5y, 6x+6y, 5x+5y
f(x) + f(y) = -5x, 6x, 5x
+ -5y,6y, 5y
Does f(x + y) = f(x) + f(y) for all x, y E R? Yes, they are equal
b. f(cx) = -5cx, 6cx, 5cx
c(f(x)) = C
-5x, 6x, 5x
Does f(cx) = c(f(x)) for all c, x ER? Yes, they are equal
c. Is f a linear transformation? f is a linear transformation
Transcribed Image Text:]Let ƒ : R → R³ be defined by f(x) = (−5x, 6x, 5x). Is ƒ a linear transformation? a. f(x + y) = -5x-5y, 6x+6y, 5x+5y f(x) + f(y) = -5x, 6x, 5x + -5y,6y, 5y Does f(x + y) = f(x) + f(y) for all x, y E R? Yes, they are equal b. f(cx) = -5cx, 6cx, 5cx c(f(x)) = C -5x, 6x, 5x Does f(cx) = c(f(x)) for all c, x ER? Yes, they are equal c. Is f a linear transformation? f is a linear transformation
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