Let P, be the vector space of all polynomials of degree n or less in the variable . 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 { A basis for the image of D² is { }. Enter a polynomial or a comma separated list of polynomials. }. Enter a polynomial or a comma separated list of polynomials.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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Let P, be the vector space of all polynomials of degree n or less in the variable . 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
less.
A basis for the kernel of D² is {
A basis for the image of D² is {
}. Enter a polynomial or a comma separated list of polynomials.
}. Enter a polynomial or a comma separated list of polynomials.
Transcribed Image Text:Let P, be the vector space of all polynomials of degree n or less in the variable . 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 less. A basis for the kernel of D² is { A basis for the image of D² is { }. Enter a polynomial or a comma separated list of polynomials. }. Enter a polynomial or a comma separated list of polynomials.
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