Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a. f(x + y) = (7x+7y,2x+2y,-7x-7y-2) f(x) + f(y) = (7x,2x,-7x-2) + (7y,2y,-7y-2) Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx)= (7cx,2cx,-7cx-2) c(f(x)) = c 7x,2x,-7x-2 Does f(ca) = c(f(x)) for all c, xR? No, they are not equal c. Is f a linear transformation? f is not a linear transformation v

a. f(x + y) = (7x+7y,2x+2y,-7x-7y-2) f(x) + f(y) = (7x,2x,-7x-2) + (7y,2y,-7y-2) Does f(x + y) = f(x) + f(y) for all x, y ER? No, they are not equal b. f(cx)= (7cx,2cx,-7cx-2) c(f(x)) = c 7x,2x,-7x-2 Does f(ca) = c(f(x)) for all c, xR? No, they are not equal c. Is f a linear transformation? f is not a linear transformation v

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
The inputs I have are wrong a. f(x + y) = (7x+7y,2x+2y,-7x-7y-2) f(x) + f(y) = (7x,2x,-7x-2) + (7y,2y,-7y-2) Does f(x + y) = f(x) + f(y) for all x, y € R? No, they are not equal b. f(cx)= (7cx,2cx,-7cx-2) c(f(x)) = c 7x,2x,-7x-2 Does f(cx) = c(f(x)) for all c, x ER? No, they are not equal c. Is f a linear transformation? f is not a linear transformation ✓ Note: In order to get credit for this problem all answers must be correct V V
Transcribed Image Text:The inputs I have are wrong a. f(x + y) = (7x+7y,2x+2y,-7x-7y-2) f(x) + f(y) = (7x,2x,-7x-2) + (7y,2y,-7y-2) Does f(x + y) = f(x) + f(y) for all x, y € R? No, they are not equal b. f(cx)= (7cx,2cx,-7cx-2) c(f(x)) = c 7x,2x,-7x-2 Does f(cx) = c(f(x)) for all c, x ER? No, they are not equal c. Is f a linear transformation? f is not a linear transformation ✓ Note: In order to get credit for this problem all answers must be correct V V
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS