Letf: R² → R be defined by f((x, y)) = -3x - 7y. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) = + Does f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, Y₁ ), (x2, y₂) E R²? choose b. f(c(x, y)) = (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Isf a linear transformation? choose
Letf: R² → R be defined by f((x, y)) = -3x - 7y. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) = + Does f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, Y₁ ), (x2, y₂) E R²? choose b. f(c(x, y)) = (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose c. Isf a linear transformation? choose
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:Letf : R² → R be defined by ƒ((x, y)) = −3x – 7y. Is ƒ a linear transformation?
a. f((x₁, y₁) + (x₂, y2)) =
f((x₁, y₁)) + f((x₂, y2)) =
Does f((x₁, y₁) + (x₂, y₂)) = f((x₁, y₁)) + f((x₂, y₂)) for all (x₁, y₁), (x₂, y₂) E R²? choose
. (Enter x₁ as x1, etc.)
b. f(c(x, y)) =
c(f((x, y))) =
=
Does f(c(x, y)) = c(f((x, y))) for all c E R and all (x, y) = R²? choose
c. Isf a linear transformation? choose
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