The first four Hermite polynomials are and . These

Chapter 4, Problem 21E

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QUESTION:

The first four Hermite polynomials are \(1,2 t,-2+4 t^{2}\), and \(-12 t+8 t^{3}\). These polynomials arise naturally in the study of certain important differential equations in mathematical physics.\(^2\) Show that the first four Hermite polynomials form a basis of \(\mathbb{P}^{2}\).

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QUESTION:

The first four Hermite polynomials are \(1,2 t,-2+4 t^{2}\), and \(-12 t+8 t^{3}\). These polynomials arise naturally in the study of certain important differential equations in mathematical physics.\(^2\) Show that the first four Hermite polynomials form a basis of \(\mathbb{P}^{2}\).

ANSWER:

Solution 21EStep 1 of 2Consider the Hermite Polynomials Objective is to show that the first four Hermite polynomials form a basis of The matrix whose columns are the coordinate vectors of given Hermite Polynomials relative to the standard basis is Divide 8 to the row 4. Divide 4 to row 3. Divide 2 to row 2.

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