4. Let V = {ao+aj x+a2 x² | ao, a1, a2 E R} be a vector space of polynomialup to degree three, and p(x) = pPo+P1 x+p2 x², q(x)= qo+q1 x+q2 x² E Vthen show that< p(x), q(x) >= po.4o + pP1-q1 + P2-92defines an inner product on V.

To show that <p(x),q(x)>=p0q0+p1q1+p2q2 is an inner product on V and field is of ℝ, we need…

Let V = {ao+ai x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial up to degree three, and p(x) = po+pi x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= Po•9o + P1.qi + P2-92 defines an inner product on V.

Let V = {ao+ai x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial up to degree three, and p(x) = po+pi x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= Po•9o + P1.qi + P2-92 defines an inner product on V.

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

4. Let V = {ao+aj x+a2 x² | ao, a1, a2 E R} be a vector space of polynomial
up to degree three, and p(x) = pPo+P1 x+p2 x², q(x)
= qo+q1 x+q2 x² E V
then show that
< p(x), q(x) >= po.4o + pP1-q1 + P2-92
defines an inner product on V.

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