Answered: 4. Consider the set of functions S =…

4. Consider the set of functions S = {-3(x² – 4)°,7|x² – 4|³}. a. Show that S is a linearly independent set in C[1,3]. b. Show that S is a linearly dependent set in C[2,3].

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

4. Consider the set of functions S = {-3(x² – 4)5,7|x² – 4|5}.
a. Show that S is a linearly independent set in C[1,3].
b. Show that S is a linearly dependent set in C[2,3].

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