Let 8 be the basis of På consisting of the Hermite polynomials 1, 2t, -2+ 41 and 12t+Sttand let p Flnd the coordinate vector ofp relalive to 8. 口口□口
Let 8 be the basis of På consisting of the Hermite polynomials 1, 2t, -2+ 41 and 12t+Sttand let p Flnd the coordinate vector ofp relalive to 8. 口口□口
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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![**Basis Representation of Polynomials with Hermite Polynomials**
Let \(B\) be the basis of \(P_3\), consisting of the Hermite polynomials: \(1\), \(2t\), \(-2 + 4t^2\), and \(-12t + 8t^3\).
Given a polynomial \(p(t) = 1 - 4t^2 - 8t^2\), our objective is to find the coordinate vector of \(p\) relative to the basis \(B\).
\[
[p]_B = \begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9225fa68-a539-4743-ab4b-10a3968e5a82%2F8e326d8b-798c-4ee0-bd34-173515972b27%2Fyd5xdo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Basis Representation of Polynomials with Hermite Polynomials**
Let \(B\) be the basis of \(P_3\), consisting of the Hermite polynomials: \(1\), \(2t\), \(-2 + 4t^2\), and \(-12t + 8t^3\).
Given a polynomial \(p(t) = 1 - 4t^2 - 8t^2\), our objective is to find the coordinate vector of \(p\) relative to the basis \(B\).
\[
[p]_B = \begin{bmatrix}
\boxed{} \\
\boxed{} \\
\boxed{} \\
\boxed{}
\end{bmatrix}
\]
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