Let ƒ : R² → R be defined by ƒ((x, y)) = −7x − 9y. Is ƒ a linear transformation?
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 f((x, y)) = −7x − 9y. Is ƒ a linear
transformation?
a. f((x₁, y₁) + (x2, Y₂)) =
as x1, etc.)
f((x₁, y₁)) + f((x2, 3/2)) =
Does f((x₁, y₁) + (x2, Y2 )) = f((x₁, y₁ )) + ƒ((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(f((x, y))) for all c E R and all (x, y) = R²?
choose
c. Isf a linear transformation? choose
. (Enter X₁
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