| Let ƒ : R² → R be defined by ƒ((x, y)) = 3x + 8y − 1. 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 )) + ƒ((x2, y2)) for all (x₁, Y₁ ), (x2, Y2 ) E R²? choose الا 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. Is f a linear transformation? choose . (Enter x₁ as x1, etc.)
| Let ƒ : R² → R be defined by ƒ((x, y)) = 3x + 8y − 1. 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 )) + ƒ((x2, y2)) for all (x₁, Y₁ ), (x2, Y2 ) E R²? choose الا 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. Is f a linear transformation? choose . (Enter x₁ as x1, etc.)
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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Let ƒ : R² → R be defined by f((x, y)) = 3x + 8y − 1. Is ƒ a linear transformation?
a. f((x₁, y₁) + (x₂, y₂)) =
f((x₁, y₁)) + f((x2, y₂)) =
=
+
Does ƒ((x₁, y₁) + (x2, y2)) = f((x₁, y₁ )) + ƒ((x2, y2)) for all (x1, Y1 ), (x2, Y2 ) E R² ?
choose
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. Is f a linear transformation? choose
. (Enter x₁ as x1, etc.)
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