Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra + B)=rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O if L is a linear transformation, then L(ra) = rL(a) for all a E V %3D and scalar r. O IfL is a linear transformation, then L(a +B)3 L(@) +L(B) for all a, 8 E V.

Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra + B)=rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O if L is a linear transformation, then L(ra) = rL(a) for all a E V %3D and scalar r. O IfL is a linear transformation, then L(a +B)3 L(@) +L(B) for all a, 8 E 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
Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra +B)3rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O If L is a linear transformation, then L(ra) =rL(a) for all a E V and scalar r. O IfL is a linear transformation, then L(a+B) = L(a) +L(B) for all a, 8E V.
Transcribed Image Text:Let L: V- W be a mapping, where V and W are vector spaces. Which of the following is NOT always true? O If L(ra +B)3rL(a) + L(B) for all a, 8 E V and scalar r. then L is a linear transformation. O If L is a linear transformation, then L(ra) =rL(a) for all a E V and scalar r. O IfL is a linear transformation, then L(a+B) = L(a) +L(B) for all a, 8E V.
Expert Solution
steps

Step by step

Solved in 3 steps

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