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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddf5ff21-58c5-47d5-a217-357a5bab1bf2%2F9885284b-9932-4dae-844c-7b6134938d6c%2Fiz9jj5s_processed.jpeg&w=3840&q=75)
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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