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3 Letf : R → R³ be defined by f(x) = (x, 2x², −2x). Is ƒ a linear transformation?

3 Letf : R → R³ be defined by f(x) = (x, 2x², −2x). Is ƒ a linear transformation?

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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THIS IS WRONG AGAIN. PLEASE ANSWER IT CORRECTLY AS IM PAYING FOR THE SUBSCRIPTION

Letf: R R³ be defined by f(x) = (x, 2x², −2x). Is ƒ a linear transformation? a. f(x + y) = x+y,2(x^2+2xy+y^2),-2(x+y) f(x) + f(y) = x,2x^2,-2x + y,y^2,-2y Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx) = cx,2c^2x^2,-2cx c(f(x)) = с X,2x^2,-2x Does f(cx) = c(f(x)) for all c, x = R? No, they are not equal c. Is f a linear transformation? f is not a linear transformation
Transcribed Image Text:Letf: R R³ be defined by f(x) = (x, 2x², −2x). Is ƒ a linear transformation? a. f(x + y) = x+y,2(x^2+2xy+y^2),-2(x+y) f(x) + f(y) = x,2x^2,-2x + y,y^2,-2y Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx) = cx,2c^2x^2,-2cx c(f(x)) = с X,2x^2,-2x Does f(cx) = c(f(x)) for all c, x = R? No, they are not equal c. Is f a linear transformation? f is not a linear transformation
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