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Homework-2: Problem 1 (1 point) Let ƒ : R → R³ be defined by f(x) = (x, 8x², − 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? No, they are not equal b. f(cx) : = c(f(x)) = (0). Does f(cx) = c(f(x)) for all c, x € R? Yes, they are equal c. Is f a linear transformation? f is a linear transformation

Homework-2: Problem 1 (1 point) Let ƒ : R → R³ be defined by f(x) = (x, 8x², − 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? No, they are not equal b. f(cx) : = c(f(x)) = (0). Does f(cx) = c(f(x)) for all c, x € R? Yes, they are equal c. Is f a linear transformation? f is 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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Homework-2: Problem 1 (1 point) Let ƒ : R → R³ be defined by f(x) = (x, 8x², − 3x). Is ƒ a linear transformation? a. f(x + y) = <x+y,8(x+y)²,-3> f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx) : = c(f(x)) = (0). Does f(cx) = c(f(x)) for all c, x € R? Yes, they are equal c. Is f a linear transformation? f is a linear transformation
Transcribed Image Text:Homework-2: Problem 1 (1 point) Let ƒ : R → R³ be defined by f(x) = (x, 8x², − 3x). Is ƒ a linear transformation? a. f(x + y) = <x+y,8(x+y)²,-3> f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx) : = c(f(x)) = (0). Does f(cx) = c(f(x)) for all c, x € R? Yes, they are equal c. Is f a linear transformation? f is a linear transformation
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