Let f : R² → R be defined by f((x, y)) = 8x+2y + 2. Is ƒ a linear transformation? a. f((x₁, y₁) + (x2, Y2)): b. f(c(x, y)) = f((x1, y₁)) + f((x2, 2)) + Does f((x1, y₁) + (x2, Y2)) = ƒ((x₁, y₁)) + f((x2, y₂)) for all (x₁, y₁), (X2, Y2) € R²? choose = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose . (Enter ₁ as x1, etc.) c. Is f a linear transformation? choose >
Let f : R² → R be defined by f((x, y)) = 8x+2y + 2. Is ƒ a linear transformation? a. f((x₁, y₁) + (x2, Y2)): b. f(c(x, y)) = f((x1, y₁)) + f((x2, 2)) + Does f((x1, y₁) + (x2, Y2)) = ƒ((x₁, y₁)) + f((x2, y₂)) for all (x₁, y₁), (X2, Y2) € R²? choose = c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose . (Enter ₁ as x1, etc.) c. Is f 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
Related questions
Question
![Let f : R² → R be defined by f((x, y)) = 8x +2y + 2. Is ƒ a linear transformation?
a. f((x₁, y₁) + (x2, Y2)):
b. f(c(x, y))
=
f((x1, y₁)) + f((x2, 2)):
+
Does f((x1, y₁) + (x2, Y2)) = f((x₁, Y₁)) + f((x2, y₂)) for all (x₁, Y₁), (X2, Y2) € R²? choose
=
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose
. (Enter ₁ as x1, etc.)
c. Is f a linear transformation? choose
<](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f21868f-81f5-47ff-b0b8-24fe685287c0%2F9fca0bcd-ad0b-439c-9206-17c45d1e01f7%2Fiz87jfn_processed.png&w=3840&q=75)
Transcribed Image Text:Let f : R² → R be defined by f((x, y)) = 8x +2y + 2. Is ƒ a linear transformation?
a. f((x₁, y₁) + (x2, Y2)):
b. f(c(x, y))
=
f((x1, y₁)) + f((x2, 2)):
+
Does f((x1, y₁) + (x2, Y2)) = f((x₁, Y₁)) + f((x2, y₂)) for all (x₁, Y₁), (X2, Y2) € R²? choose
=
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose
. (Enter ₁ as x1, etc.)
c. Is f a linear transformation? choose
<
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