Problem 2.Let P3 be the vector space of all polynomials of degree 3 or less in the variable r. Let2 - r + 2?6 – 3x + 3x? - 3z,2+ 2? – z',P1(z)P2(x)p3(2)P1(z)3 - z + 2x? – 273and let C = {p1(r), p2(2), pa(r), pa(z)}.a. Use coordinate representations with respect to the basis B = {1, z, r?, z'} to determine whether the set C forms a basis for P3. choose%3Db. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials.{}c. The dimension of span(C) is

In this question, we check the given set forms a basis or not then after we use elementary…

Answered: Let P3 be the vector space of all…

Let P3 be the vector space of all polynomials of degree 3 or less in the variable z. Let 2 - z+z? - r', 6 – 3z + 3r? - 3z, 2+z? - z, P1(z) %3D P2(z) P3(z) P:(z) %3D 3 -z+ 2z? - 2z³ %3!

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

Problem 2.
Let P3 be the vector space of all polynomials of degree 3 or less in the variable r. Let
2 - r + 2?
6 – 3x + 3x? - 3z,
2+ 2? – z',
P1(z)
P2(x)
p3(2)
P1(z)
3 - z + 2x? – 273
and let C = {p1(r), p2(2), pa(r), pa(z)}.
a. Use coordinate representations with respect to the basis B = {1, z, r?, z'} to determine whether the set C forms a basis for P3. choose
%3D
b. Find a basis for span(C). Enter a polynomial or a comma separated list of polynomials.
{
}
c. The dimension of span(C) is

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