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2. Let p1(t) = 1, p2(t) = 2t, p3 (t) = -2+4t² and p4(t) = –12t + 8t3 be polynomials is P3 (these are the first four Hermite polynomials). Consider the set B = {p1(t), p2(t), p3(t), p4(t)}. (a) Show that B is a basis for P3. (b) Determine the B-coordinate of the polynomial g(t) = 1+ 4t + 7t2.

2. Let p1(t) = 1, p2(t) = 2t, p3 (t) = -2+4t² and p4(t) = –12t + 8t3 be polynomials is P3 (these are the first four Hermite polynomials). Consider the set B = {p1(t), p2(t), p3(t), p4(t)}. (a) Show that B is a basis for P3. (b) Determine the B-coordinate of the polynomial g(t) = 1+ 4t + 7t2.

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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2. Let pi(t) = 1, P2 (t) = 2t, p3(t) = -2+ 4t² and p4(t) = –12t + 8t³ be polynomials is P3 (these are the first four Hermite polynomials). Consider the set B = {p1(t), p2(t), p3(t), p4(t)}. (a) Show that B is a basis for P3. (b) Determine the B-coordinate of the polynomial g(t) = 1+ 4t + 7t².
Transcribed Image Text:2. Let pi(t) = 1, P2 (t) = 2t, p3(t) = -2+ 4t² and p4(t) = –12t + 8t³ be polynomials is P3 (these are the first four Hermite polynomials). Consider the set B = {p1(t), p2(t), p3(t), p4(t)}. (a) Show that B is a basis for P3. (b) Determine the B-coordinate of the polynomial g(t) = 1+ 4t + 7t².
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