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Use the standard basis for P2, B = {1, t, t²}, and the coordinate mapping to show that 10 – 12t – 25t² is in H, and use this to write 10 – 12t – 25t² as a linear combination of P¡(t), P2(t), and, p3(t). Please show all work! Is the polynomial 3 – 3t in H? If you answer yes, write 3 – 3t as a linear combination of P;(t), p2(t), and, p3(t). If no, make sure your work is clear as to why not. Does the set of polynomials {-1+ 3t – 21², 4 – 10t + 3t², 4 – 8t – 21²} span P,? Why

Use the standard basis for P2, B = {1, t, t²}, and the coordinate mapping to show that 10 – 12t – 25t² is in H, and use this to write 10 – 12t – 25t² as a linear combination of P¡(t), P2(t), and, p3(t). Please show all work! Is the polynomial 3 – 3t in H? If you answer yes, write 3 – 3t as a linear combination of P;(t), p2(t), and, p3(t). If no, make sure your work is clear as to why not. Does the set of polynomials {-1+ 3t – 21², 4 – 10t + 3t², 4 – 8t – 21²} span P,? Why

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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Problem 3: Consider the set of polynomials {-1+3t – 21², 4 – 10t + 3t², 4 – 8t – 21²} . Let p¡(t) = – 1 + 3t – 21², p2(t) = 4 – 10t + 3ť², and p3(t) = 4 – 8t – 21². Let H = span {p,(t), P2(t), P3(t)}, which is a subset of P,.
Transcribed Image Text:Problem 3: Consider the set of polynomials {-1+3t – 21², 4 – 10t + 3t², 4 – 8t – 21²} . Let p¡(t) = – 1 + 3t – 21², p2(t) = 4 – 10t + 3ť², and p3(t) = 4 – 8t – 21². Let H = span {p,(t), P2(t), P3(t)}, which is a subset of P,.
Use the standard basis for P, B = {1, t, t2}, and the coordinate mapping to show that 10 – 12t – 25t² is in H, and use this to write 10 – 12t – 25t? as a linear combination of P¡(t), p2(t), and, p3(t). Please show all work! Is the polynomial 3 – 3t in H? If you answer yes, write 3 – 3t as a linear combination of P,(t), P2(t), and, p3(t). If no, make sure your work is clear as to why not. - Does the set of polynomials {-1+ 3t – 2t?, 4 10t + 3t2, 4 – 8t – 2t2} span P,? Why -
Transcribed Image Text:Use the standard basis for P, B = {1, t, t2}, and the coordinate mapping to show that 10 – 12t – 25t² is in H, and use this to write 10 – 12t – 25t? as a linear combination of P¡(t), p2(t), and, p3(t). Please show all work! Is the polynomial 3 – 3t in H? If you answer yes, write 3 – 3t as a linear combination of P,(t), P2(t), and, p3(t). If no, make sure your work is clear as to why not. - Does the set of polynomials {-1+ 3t – 2t?, 4 10t + 3t2, 4 – 8t – 2t2} span P,? Why -
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