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Letƒ : R → R³ be defined byƒ(x) = (x, −7x², 5x). Is ƒ a linear transformation? a. f(x+ y) = f(x) + f(y) = Does ƒ(x+y) = f(x) + f(y) for all x, y ER? choose b. f(cx) = c(f(x)) = = Does ƒ(cx) = c(f(x)) for all c, x € R? choose c. Isf a linear transformation? choose

Letƒ : R → R³ be defined byƒ(x) = (x, −7x², 5x). Is ƒ a linear transformation? a. f(x+ y) = f(x) + f(y) = Does ƒ(x+y) = f(x) + f(y) for all x, y ER? choose b. f(cx) = c(f(x)) = = Does ƒ(cx) = c(f(x)) for all c, x € R? choose c. Isf 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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Letf : R → R³ be defined by ƒ(x) = (x, −7x²,5x). 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 ER? choose b. f(cx) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x ER? choose c. Isf a linear transformation? choose ←
Transcribed Image Text:Letf : R → R³ be defined by ƒ(x) = (x, −7x²,5x). 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 ER? choose b. f(cx) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x ER? choose c. Isf a linear transformation? choose ←
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