9. Let E be àń extension field of F, and let a, ß e E. Suppose a is transcendental over F but algebraic over F (P). Show that B is algebraic over F(@).
9. Let E be àń extension field of F, and let a, ß e E. Suppose a is transcendental over F but algebraic over F (P). Show that B is algebraic over F(@).
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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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Section 29 number 30
![29. Let E be an extension field of F, and let a, BE E. Suppose a is transcendental over F but algebraic over F(ß).
Show that B is algebraic over F (a).
30. Let E be an extension field of a finite field F, where F has q elements. Let a e E be algebraic over F of degree
n. Prove that F (@) has q" elements.
31 a Show that there exists an irreducible polynomial of degree 3 in Z3[x].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4dd8e23-ab66-4b24-8e54-a64daec9031c%2Fc55dd42d-f890-4d4b-8ef4-bb91f24ab368%2Fuu45ayl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:29. Let E be an extension field of F, and let a, BE E. Suppose a is transcendental over F but algebraic over F(ß).
Show that B is algebraic over F (a).
30. Let E be an extension field of a finite field F, where F has q elements. Let a e E be algebraic over F of degree
n. Prove that F (@) has q" elements.
31 a Show that there exists an irreducible polynomial of degree 3 in Z3[x].
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