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Letf : R² → R be defined by f((x, y)) = 8x + 5y + 1. Isf 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), (2, 2) 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 ER and all (x, y) = R²? choose c. Isf a linear transformation? choose +

Letf : R² → R be defined by f((x, y)) = 8x + 5y + 1. Isf 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), (2, 2) 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 ER and all (x, y) = R²? choose c. Isf a linear transformation? choose +

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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Letf: R²- → R be defined by f((x, y)) = 8x + 5y + 1. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) = b. f(c(x, y)) = f((x₁, y₁)) + f((x₂, y₂)) = + Does f((x₁, y1) + (x2, y₂)) = f((x₁, y₁ )) + f((x₂, y₂)) for all (x₁, y₁), (₂, ₂) E R²? choose . (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose c. Isf a linear transformation? choose + +
Transcribed Image Text:Letf: R²- → R be defined by f((x, y)) = 8x + 5y + 1. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) = b. f(c(x, y)) = f((x₁, y₁)) + f((x₂, y₂)) = + Does f((x₁, y1) + (x2, y₂)) = f((x₁, y₁ )) + f((x₂, y₂)) for all (x₁, y₁), (₂, ₂) E R²? choose . (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose c. Isf a linear transformation? choose + +
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