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Consider polynomials with degree less than or equal to n. We can think that each polynomial p(x)=a+a, x+...+a,x" is a vector in the n+1 dimensional vector space, with components (a,,a,,a,) and basis (1,x,...,x). Find the representation of the d operator in this vector dx space.

Consider polynomials with degree less than or equal to n. We can think that each polynomial p(x)=a+a, x+...+a,x" is a vector in the n+1 dimensional vector space, with components (a,,a,,a,) and basis (1,x,...,x). Find the representation of the d operator in this vector dx space.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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Consider polynomials with degree less than or equal to n. We can think that each polynomial p(x)=a+a, x+...+a," is a vector in the n+1 dimensional vector space, with components (a,,a,,a,) and basis (1,x,...,x). Find the representation of the operator in this vector dx space.
Transcribed Image Text:Consider polynomials with degree less than or equal to n. We can think that each polynomial p(x)=a+a, x+...+a," is a vector in the n+1 dimensional vector space, with components (a,,a,,a,) and basis (1,x,...,x). Find the representation of the operator in this vector dx space.
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