Let ƒ : R² → R be defined by ƒ((x, y)) = 2x + 5y + 3. Is ƒ a linear transformation? a. f((x1, y₁) + (x2, y₂)) = 10 f((x₁, y₁)) +ƒ((x2, Y2)) = . (Enter x₁ as x1, etc.) = 8 + 5 Does f((x₁, y₁) + (x2, y2)) = f((x1, y₁)) +ƒ((x2, y2)) for all (x₁, y₁), (x2, y2) E R²? No, they are not equal b. f(c(x, y)) = 13 c(f((x, y))) = 2 8 Does ƒ(c(x, y)) = c(fƒ((x, y))) for all c E R and all (x, y) = R²? No, they are not equal c. Is ƒ a linear transformation? f is not a linear transformation
Let ƒ : R² → R be defined by ƒ((x, y)) = 2x + 5y + 3. Is ƒ a linear transformation? a. f((x1, y₁) + (x2, y₂)) = 10 f((x₁, y₁)) +ƒ((x2, Y2)) = . (Enter x₁ as x1, etc.) = 8 + 5 Does f((x₁, y₁) + (x2, y2)) = f((x1, y₁)) +ƒ((x2, y2)) for all (x₁, y₁), (x2, y2) E R²? No, they are not equal b. f(c(x, y)) = 13 c(f((x, y))) = 2 8 Does ƒ(c(x, y)) = c(fƒ((x, y))) for all c E R and all (x, y) = R²? No, they are not equal c. Is ƒ a linear transformation? f is not a linear transformation
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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Transcribed Image Text:→ R be defined by f((x, y)) = 2x + 5y + 3. Is ƒ a linear transformation?
Letf: R².
a. f((x₁, y₁) + (x2, ₂)) = 10
f((x₁, y₁)) + f((x2, y₂)) =
. (Enter x₁ as x1, etc.)
= 8
+ 5
Does f((x₁, y₁) + (x2, y2)) = f((x₁, y₁)) + ƒ((x2, y2)) for all (x1, Y1), (x2, Y2) € R²?
No, they are not equal
b. f(c(x, y)) = 13
c(f((x, y))) = 2
8
Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? No, they are not equal
c. Is f a linear transformation? f is not a linear transformation
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