Answered: 6. Let F be a field and suppose that y…

6. Let F be a field and suppose that y : F → F is a map from F to F that satisfies the property p(ab) = 4(a)p(b) for all a, b E F. Show that p(1) is either 0 or 1. (Hint: 1=1·1.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 5E: Let F be a field and f(x)=a0+a1x+...+anxnF[x]. Prove that x1 is a factor of f(x) if and only if...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Please solve this question with a good explanation. It is Linear Algebra question.

6. Let F be a field and suppose that y : F → F is a map from F to F that
satisfies the property p(ab) = 4(a)p(b) for all a, b E F. Show that p(1)
is either 0 or 1. (Hint: 1=1·1.)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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