Let P2 be the vector space of all real polynomials of degree at most 2. Let p1, P2, P3 E P2 be given by p1 (x) = 2, p2(x) = x + 2x², and p3(x) = 6x + aa². a) (You are free to assume that the functions 1, x and x? are linearly independent.) b) combination of p1, P2 Find the condition on a e R that ensures that {P1, P2, P3} is a basis for P2. In the case that a = 6, write the function p(x) = 2 – x + x2 as a linear and P3.

Let P2 be the vector space of all real polynomials of degree at most 2. Let p1, P2, P3 E P2 be given by p1 (x) = 2, p2(x) = x + 2x², and p3(x) = 6x + aa². a) (You are free to assume that the functions 1, x and x? are linearly independent.) b) combination of p1, P2 Find the condition on a e R that ensures that {P1, P2, P3} is a basis for P2. In the case that a = 6, write the function p(x) = 2 – x + x2 as a linear and P3.

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

Let P2 be the vector space of all real polynomials of degree at most 2. Let p1, P2, P3 E P2 be
given by p1(x) = 2, p2(x) = x + 2x², and p3(x) = 6x + ax².
а)
(You are free to assume that the functions 1, x and x? are linearly independent.)
b)
combination of p1, P2 and p3.
%3D
Find the condition on a e R that ensures that {P1, P2, P3} is a basis for P2.
In the case that a =
6, write the function p(x) = 2 – x + x² as a linear
%D

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