**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 $B$.\[[p]_B = \begin{bmatrix}\boxed{} \\\boxed{} \\\boxed{} \\\boxed{}\end{bmatrix}\]

Suppose V is a finite dimensional vector space over field and is a basis. Then, every element of…

Answered: Let 8 be the basis of På consisting of…

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

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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**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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