Let f: R² → R be defined by f((x, y)) = 8x +9y. Is f 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, 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 = R and all (x, y) = R²? choose c. Is f a linear transformation? choose . (Enter ₁ as x1, etc.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f: R² → R be defined by f((x, y)) = 8x +9y. Is f a linear transformation?
a. f((x1, y₁) + (x2, Y₂)) =
f((x1, y₁)) + f((x2, Y2)) =
+
Does f((x1, y₁) + (x2, Y₂)) = ƒ((X₁,Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, Y2) € R²? choose
E
b. f(c(x, y)):
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose
c. Is f a linear transformation? choose
. (Enter ₁ as x1, etc.)
Transcribed Image Text:Let f: R² → R be defined by f((x, y)) = 8x +9y. Is f a linear transformation? a. f((x1, y₁) + (x2, Y₂)) = f((x1, y₁)) + f((x2, Y2)) = + Does f((x1, y₁) + (x2, Y₂)) = ƒ((X₁,Y₁)) + f((x2, y₂)) for all (x₁, y₁), (2, Y2) € R²? choose E b. f(c(x, y)): c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c = R and all (x, y) = R²? choose c. Is f a linear transformation? choose . (Enter ₁ as x1, etc.)
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