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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.

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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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.
Transcribed Image Text: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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