Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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
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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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