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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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