Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² + 3t³ + t², 1+t+21² + 3t³ + 2t¹} (a)!'. Write the coordinate vector of each polynomial in S in terms of the standard basis for P4. (b) ;) Determine whether the vectors in S are linearly independent in P4? Do they span P₁?
Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² + 3t³ + t², 1+t+21² + 3t³ + 2t¹} (a)!'. Write the coordinate vector of each polynomial in S in terms of the standard basis for P4. (b) ;) Determine whether the vectors in S are linearly independent in P4? Do they span P₁?
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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Transcribed Image Text:Problem 10. Consider the following set of polynomials in P4:
S = {1+3t + t, 1+t+2t + 3t", t+t² + 3t + t*, 1+t+ 2t? + 3t + 2t*}
%3D
I Write the coordinate vector of each polynomial in S in terms of the
(a) .
standard basis for P4.
(b)
they span P?
:) Determine whether the vectors in S are linearly independent in P1? Do
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