Let f: R→ R³ be defined by f(x) = (4x, 8x, -7x). Is f a linear transformation? a. f(x + y) = (4x+4y,8x+8y,-7x-7y) f(x) + f(y) = (4x,8x,-7x) + (4y,8y,-7y) Does f(x + y) = f(x) + f(y) for all x, y € R? Yes, they are equal b. f(cx) = (4(cx),8(cx), -7(cx)) c(f(x)) = с 4x,8x,-7x 1). Does f(cx) = c(f(x)) for all c, x E R? Yes, they are equal c. Is f a linear transformation? f is a linear transformation +
Let f: R→ R³ be defined by f(x) = (4x, 8x, -7x). Is f a linear transformation? a. f(x + y) = (4x+4y,8x+8y,-7x-7y) f(x) + f(y) = (4x,8x,-7x) + (4y,8y,-7y) Does f(x + y) = f(x) + f(y) for all x, y € R? Yes, they are equal b. f(cx) = (4(cx),8(cx), -7(cx)) c(f(x)) = с 4x,8x,-7x 1). Does f(cx) = c(f(x)) for all c, x E R? Yes, they are equal c. Is f a 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
Related questions
Question
HI. I got the answers wrong. Please assist me
Transcribed Image Text:Entered
(4*x+4*y,8*x+8*y,-7*x-7*y)
(4*x,8*x,-7*x) + (4*y,8*y,-7*y)
Yes, they are equal
(4*c*x,8*c*x,-7*c*x)
c ( 4*x, 8*x, -7*x)
Yes, they are equal
f is a linear transformation
b. f(cx) =
(4x+4y,8x+8y,-7x-7y)
Answer Preview
(4x + 4y, 8x + 8y, −7x − 7y)
(4(cx),8(cx),-7(cx))
(4x, 8x, -7x) + (4y, 8y, -7y)
Yes, they are equal
(4cx, 8cx, -7cx)
c(4x, 8x, -7x)
Yes, they are equal
a. f(x + y) =
f(x) + f(y) = (4x,8x,-7x)
+ (4y,8y,-7y)
Does f(x + y) = f(x) + f(y) for all x, y E R? Yes, they are equal
f is a linear transformation
Let ƒ : R → R³ be defined by f(x) = (4x, 8x, −7x). Is ƒ a linear transformation?
c(f(x)) = C
4x,8x,-7x
Does f(cx) = c(f(x)) for all c, x ER? Yes, they are equal
In answer 1:
c. Is f a linear transformation? f is a linear transformation
In answer 2:
In answer 2:
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Your answer isn't a formula that returns a vector
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Your answer isn't a formula that returns a vector
(it looks like a formula that returns a point)
Your answer isn't a formula that returns a vector
(it looks like a formula that returns a list of numbers)
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