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23. Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic tó the vector space F" of Exercise 19.

23. Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic tó the vector space F" of Exercise 19.

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
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Section 30 number 23 (use number 19 to help)
282 Part VI Extension Fields 19. Generalize Example 30.2 to obtain the vector space F" of ordered n-tuples of elements of F over the field F, for any field F. What is a basis for F"?
Transcribed Image Text:282 Part VI Extension Fields 19. Generalize Example 30.2 to obtain the vector space F" of ordered n-tuples of elements of F over the field F, for any field F. What is a basis for F"?
esh (This result is straightforward to prove, being practically the regarded as the fundamental existence theorem for a simultaneous solution of a system of linear equations.) b. From part (a), show that if = m and falj unique soludon. |is a basis for F" then the system always has a 23. Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic to the vector space F" of Exercise 19. an of V
Transcribed Image Text:esh (This result is straightforward to prove, being practically the regarded as the fundamental existence theorem for a simultaneous solution of a system of linear equations.) b. From part (a), show that if = m and falj unique soludon. |is a basis for F" then the system always has a 23. Prove that every finite-dimensional vector space V of dimension n over a field F is isomorphic to the vector space F" of Exercise 19. an of V
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