Do write Answer on paper with good handwriting and clear photo. Thank you Consider P3, the vector space of all polynomials with real polynomials coefficients with degreeless than or equal to 3 (for example, f(x) = Tr +5 is in P3).1. Give a basis for P3.2. What is the dimension of P3?3. Let (p(x), q(x)) = deg(p(x)) + deg(q(x)).Determine if (, ) is an inner product on P3. Explain your answer.

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Consider P3, the vector space of all polynomials with real polynomials coefficients with degree ess than or equal to 3 (for example, f(x) = Tx3 + 5 is in Ps). 1. Give a basis for P3. 2. What is the dimension of P3? 3. Let (p(x), q(x)) = deg(p(x)) + deg(q(x)). Determine if (, :) is an iner product on P3. Explain your answer.

Consider P3, the vector space of all polynomials with real polynomials coefficients with degree ess than or equal to 3 (for example, f(x) = Tx3 + 5 is in Ps). 1. Give a basis for P3. 2. What is the dimension of P3? 3. Let (p(x), q(x)) = deg(p(x)) + deg(q(x)). Determine if (, :) is an iner product on P3. Explain your answer.

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 4E: Write each of the following polynomials as a products of its leading coefficient and a finite number...

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Do write Answer on paper with good handwriting and clear photo. Thank you

Consider P3, the vector space of all polynomials with real polynomials coefficients with degree
less than or equal to 3 (for example, f(x) = Tr +5 is in P3).
1. Give a basis for P3.
2. What is the dimension of P3?
3. Let (p(x), q(x)) = deg(p(x)) + deg(q(x)).
Determine if (, ) is an inner product on P3. Explain your answer.

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