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Question 2 dependent in P[r]. Prove that the polynomials 2+2r-1, x² +1 and x² + are linearly

Question 2 dependent in P[r]. Prove that the polynomials 2+2r-1, x² +1 and x² + are linearly

Advanced Engineering Mathematics
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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Question 2 dependent in P[r]. Prove that the polynomials r2+2r-1, x²+1 and x² + are linearly
Transcribed Image Text:Question 2 dependent in P[r]. Prove that the polynomials r2+2r-1, x²+1 and x² + are linearly
Expert Solution
Step 1

A set of vectors { v1 , v2 , . . . . . . , vn } is linearly dependent if any one vector vi can be written as a linear combination of other vectors. 

       i.e., if vi = a1v1 + a2v2 + . . . . . . + ai-1vi-1 + ai+1vi+1 + . . . . . . + anvn 

           For some scalars a1, a2,. . . . . , an .

           

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