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The first four Hermite polynomials are 1,2t,−2+4t²,−12t + 8t³ and arise as solutions to certain differential equations. Let B be the set containing these four polynomials, i.e. B = {1,2t, −2+4t², −12t+8t³}. a Show that B is a basis for P3. b Find the coordinate vector of p(t) = 7 − 12t − 8t² + 12t³ relative to B.

The first four Hermite polynomials are 1,2t,−2+4t²,−12t + 8t³ and arise as solutions to certain differential equations. Let B be the set containing these four polynomials, i.e. B = {1,2t, −2+4t², −12t+8t³}. a Show that B is a basis for P3. b Find the coordinate vector of p(t) = 7 − 12t − 8t² + 12t³ relative to B.

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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The first four Hermite polynomials are 1,2t,−2+4t²,−12t + 8t³ and arise as solutions to certain differential equations. Let B be the set containing these four polynomials, i.e. B = {1,2t, −2+4t², −12t+8t³}. a Show that B is a basis for P3. b Find the coordinate vector of p(t) = 7 – 12t – 8t² + 12t³ relative to B.
Transcribed Image Text:The first four Hermite polynomials are 1,2t,−2+4t²,−12t + 8t³ and arise as solutions to certain differential equations. Let B be the set containing these four polynomials, i.e. B = {1,2t, −2+4t², −12t+8t³}. a Show that B is a basis for P3. b Find the coordinate vector of p(t) = 7 – 12t – 8t² + 12t³ relative to B.
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