Let Pn be the vector space of all polynomials of degree n or less in the variable æ. Let D² : P4 → P2 be the linear transformation that takes a polynomial to its second derivative. That is, D²(p(x)) = p" (x) for any polynomial p(æ) of degree 4 or less. A basis for the kernel of D² is { }. Enter a polynomial or a comma separated list of polynomials.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
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Let Pn be the vector space of all polynomials of degree n or less in the variable æ. Let D² : P4 → P2 be the linear
transformation that takes a polynomial to its second derivative. That is, D² (p(x)) = p" (x) for any polynomial p(x) of degree
4 or less.
A basis for the kernel of D² is {
8, }. Enter a polynomial or a comma separated list of polynomials.
Transcribed Image Text:Let Pn be the vector space of all polynomials of degree n or less in the variable æ. Let D² : P4 → P2 be the linear transformation that takes a polynomial to its second derivative. That is, D² (p(x)) = p" (x) for any polynomial p(x) of degree 4 or less. A basis for the kernel of D² is { 8, }. Enter a polynomial or a comma separated list of polynomials.
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