Consider the set $ S = \{x^3 + x^2, x^2 + x, x + 1, 2\} $ in $ P_3(x) $. Here $ P_3(x) $ is a vector space containing polynomials of degree less than or equal to 3.(a) [Redacted text] Is the set $ S $ linearly independent? Justify your answer.(b) [Redacted text] Does the set $ S $ span $ P_3(x) $? Justify your answer.

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Consider the set S = {r³ +x², x² + x,x + 1,2} in P3(). Here P3(r) is a vector space containing polynomials of degree less than or equal to 3. (a) | Is the set S linearly independent? Justify your answer. (b) Does the set S span P3(r)? Justify your answer.

Consider the set S = {r³ +x², x² + x,x + 1,2} in P3(). Here P3(r) is a vector space containing polynomials of degree less than or equal to 3. (a) | Is the set S linearly independent? Justify your answer. (b) Does the set S span P3(r)? Justify your answer.

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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Concept explainers

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

Consider the set $ S = \{x^3 + x^2, x^2 + x, x + 1, 2\} $ in $ P_3(x) $. Here $ P_3(x) $ is a vector space containing polynomials of degree less than or equal to 3.

(a) [Redacted text] Is the set $ S $ linearly independent? Justify your answer.

(b) [Redacted text] Does the set $ S $ span $ P_3(x) $? Justify your answer.

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