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Let R[x] be the set of all expressions a = ao+ajx+a2x² + ……=£a;x ....- i=0 where a¡ E IR for all nonnegative integers i. Informally, an element of R[x] is like a polynomial except that it can have infinitely many terms. (a) Carefully write down definitions of addition and multiplication operations for R[x], analogous to the definitions for R[x] in the notes. Given a, b e R[x], your defi- nitions should indicate what each coefficient of the sum a +b and product ab is.

Let R[x] be the set of all expressions a = ao+ajx+a2x² + ……=£a;x ....- i=0 where a¡ E IR for all nonnegative integers i. Informally, an element of R[x] is like a polynomial except that it can have infinitely many terms. (a) Carefully write down definitions of addition and multiplication operations for R[x], analogous to the definitions for R[x] in the notes. Given a, b e R[x], your defi- nitions should indicate what each coefficient of the sum a +b and product ab is.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 22E: Let be the set of all elements of that have one row that consists of zeros and one row of the form...
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Let IR[:] be the set of all expressions a = ao +ajx+azx²+= i=0 where a; e R for all nonnegative integers i. Informally, an element of R[x] is like a polynomial except that it can have infinitely many terms. (a) Carefully write down definitions of addition and multiplication operations for R[x], analogous to the definitions for R[x] in the notes. Given a, b E R[x], your defi- nitions should indicate what each coefficient of the sum a +b and product ab is.
Transcribed Image Text:Let IR[:] be the set of all expressions a = ao +ajx+azx²+= i=0 where a; e R for all nonnegative integers i. Informally, an element of R[x] is like a polynomial except that it can have infinitely many terms. (a) Carefully write down definitions of addition and multiplication operations for R[x], analogous to the definitions for R[x] in the notes. Given a, b E R[x], your defi- nitions should indicate what each coefficient of the sum a +b and product ab is.
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