4. a. Let V be a finite-dimensional vector space and let T : V → V be linear. Show that if T is one-to-one, then T is onto. b. Give an example of a function f: RR which is one-to-one but not onto. Why does this not contradict the Rank-Nullity Theorem?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
4.
a. Let V be a finite-dimensional vector space and let T : V → V be linear. Show that if
T is one-to-one, then T is onto.
b. Give an example of a function f: RR which is one-to-one but not onto. Why does
this not contradict the Rank-Nullity Theorem?
Transcribed Image Text:4. a. Let V be a finite-dimensional vector space and let T : V → V be linear. Show that if T is one-to-one, then T is onto. b. Give an example of a function f: RR which is one-to-one but not onto. Why does this not contradict the Rank-Nullity Theorem?
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
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,