Let f: R² → R be defined by f((x, y)) = 7x - 5y. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) (Enter x₁ as x1, etc.) f((x₁, y₁)) + f((x2, Y2)) = + Does = f((x₁, y₁) + (x2, Y2)) for all (x1, y₁), (x2, Y2) € R²? choose b. f(c(x, y)) = = c(f((x, y))) = f((x₁, y₁)) + f((x2, y2)) Does f(c(x, y)) = c(f((x, y))) for all cЄR and all (x, y) = R²? choose c. Is f a linear transformation? choose
Let f: R² → R be defined by f((x, y)) = 7x - 5y. Is f a linear transformation? a. f((x₁, y₁) + (x2, y₂)) (Enter x₁ as x1, etc.) f((x₁, y₁)) + f((x2, Y2)) = + Does = f((x₁, y₁) + (x2, Y2)) for all (x1, y₁), (x2, Y2) € R²? choose b. f(c(x, y)) = = c(f((x, y))) = f((x₁, y₁)) + f((x2, y2)) Does f(c(x, y)) = c(f((x, y))) for all cЄR and all (x, y) = R²? choose 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
ƒ((x, y)) = 7x − 5y. Is ƒ a linear
-
transformation?
a. f((x₁, y₁) + (x₂, Y2)) =
=
(Enter x₁ as x1, etc.)
f((x1, y₁)) + f((x2, Y2)) =
+
Does
f((x1, y1₁) + (x2, Y2)) = f((x1, Y₁)) + f((x2, Y2))
for all (x1, y₁), (x2, Y₂) = R²?
choose
b. f(c(x, y)) =
c(f((x, y))) =
Does f(c(x, y)) = c(ƒ((x, y))) for all
cЄR and all (x, y) = R²?
choose
c. Is f a linear transformation?
choose](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b030cd5-5424-4c4c-9fb9-bb5124dfa56d%2F457bf43a-aa8d-4ca0-b44d-ed8da7ddf591%2Fymrcows_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f : R² → R be defined by
ƒ((x, y)) = 7x − 5y. Is ƒ a linear
-
transformation?
a. f((x₁, y₁) + (x₂, Y2)) =
=
(Enter x₁ as x1, etc.)
f((x1, y₁)) + f((x2, Y2)) =
+
Does
f((x1, y1₁) + (x2, Y2)) = f((x1, Y₁)) + f((x2, Y2))
for all (x1, y₁), (x2, Y₂) = R²?
choose
b. f(c(x, y)) =
c(f((x, y))) =
Does f(c(x, y)) = c(ƒ((x, y))) for all
cЄR and all (x, y) = R²?
choose
c. Is f a linear transformation?
choose
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