Consider the vector space V of all the real polynomials of degree less than or equal to three, p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.
Consider the vector space V of all the real polynomials of degree less than or equal to three, p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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Consider the
p(x) = ax^3 + b x^2 + c x + d,
and consider the linear transformation T: V ------> V given by the derivative,
i.e., T( p ) = p' = 3ax^2 + 2 b x + c.
Find the eigenvalues and eigenvectors of this transformation.
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