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Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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 ER? choose b. f(cx) = = = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose

Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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 ER? choose b. f(cx) = = = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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 € R? choose b. f(cx): = = = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
Transcribed Image Text:Let f: R → R³ be defined by f(x) = (x, 6x², 3x). 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 € R? choose b. f(cx): = = = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
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