be defined by J Ja linear transformation? a. f(x + y) : <-4x-4y,-3x-3y, 7x-7y-4>| + <-4x,-3x,7y-4> Does f(x + y) = f(x)+ f(y) for all æ, y e R? Yes, they are equal f(x) + f(y) <-4x,-3x,7x-4> b. f(cz) = <-4cx, -3cx, -4+7cx> c(f(x)) = «-4х, -3х, 7х-4> Does f(ca) = c(f(x)) for all c, æ E R? Yes, they are equal c. Is fa linear transformation? f is a linear transformation
be defined by J Ja linear transformation? a. f(x + y) : <-4x-4y,-3x-3y, 7x-7y-4>| + <-4x,-3x,7y-4> Does f(x + y) = f(x)+ f(y) for all æ, y e R? Yes, they are equal f(x) + f(y) <-4x,-3x,7x-4> b. f(cz) = <-4cx, -3cx, -4+7cx> c(f(x)) = «-4х, -3х, 7х-4> Does f(ca) = c(f(x)) for all c, æ E R? Yes, they are equal c. Is fa linear transformation? f is 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:Let f:R → R° be defined by f(x) =(-4x,–3x, 7x – 4). Is fa linear transformation?
a. f(x + y) = <-4x-4y,-3x-3y, 7x-7y-4>|
f(x) + f(y)
= <-4x,-3x,7x-4>
+ <-4x,-3x,7y-4>
Does f(r+ y) = f(x)+f(y) for all z, Y E R? Yes, they are equal
b. f (cz) 3D <-4сх, -Зсх, -4+7сх>
c(f(x)) = c
<-4х, -3х, 7х-4>
Does f(cz) = c(f(x)) for all c, x E R? Yes, they are equal
c. Is fa linear transformation? fis a linear transformation
>
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