Let f: R→ R³ be defined by f(z) = (8z, 5x,-92). Is f a linear transformation? a. f(x + y) = f(x) + f(y) = Does f(x + y) = f(x) + f(y) for all z, y = R? choose b. f(cz) = c(f(x)) = Does f(cz) = c(f(x)) for all c, z = R? choose c. Is f a linear transformation? choose

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
icon
Related questions
Question
Let f: R → R³ be defined by f(x) = (8x, 5x, -9x). Is ƒ a linear transformation?
a f(x + y)
f(x) + f(y) =
+
Does f(x + y) = f(x) + f(y) for all z, y € R? choose
b. f(cz) =
c(f(x)) =
Does f(cz) = c(f(x)) for all c, z € R? choose
c. Is f a linear transformation? choose
Transcribed Image Text:Let f: R → R³ be defined by f(x) = (8x, 5x, -9x). Is ƒ a linear transformation? a f(x + y) f(x) + f(y) = + Does f(x + y) = f(x) + f(y) for all z, y € R? choose b. f(cz) = c(f(x)) = Does f(cz) = c(f(x)) for all c, z € R? choose c. Is f a linear transformation? choose
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage