Let f: R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = fƒ(x) + f(y) for all x, y < R? choose b. f(cz) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? choose c. Is f a linear transformation? choose
Let f: R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation? a. f(x + y) = f(x) + f(y) = + Does f(x + y) = fƒ(x) + f(y) for all x, y < R? choose b. f(cz) = c(f(x)) = Does f(cx) = c(f(x)) for all c, x = R? 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
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please write answer as a formula that returns a
![Let f : R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation?
a. f(x + y)
=
f(x) + f(y)
+
Does f(x + y)= f(x) + f(y) for all x, y = R? choose
b. f(cx) =
=
c(f(x)) =
Does f(cx) = c(f(x)) for all c, x ER? choose
c. Is f a linear transformation? choose](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84504046-073c-4202-8178-d38af176ff2d%2F95f1505a-a0eb-4ecb-916b-62856b605284%2F9qofwwl_processed.png&w=3840&q=75)
Transcribed Image Text:Let f : R → R³ be defined by f(x) = (8x, -7x, -9x). Is ƒ a linear transformation?
a. f(x + y)
=
f(x) + f(y)
+
Does f(x + y)= f(x) + f(y) for all x, y = R? choose
b. f(cx) =
=
c(f(x)) =
Does f(cx) = c(f(x)) for all c, x ER? choose
c. Is f a linear transformation? choose
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