Let P, be the vector space of all polynomials of degree n or less in the variable x. Let D: P3 + P2 be the linear transformation definec by D(p(x)) = p'(x). That is, D is the derivative operator. Let {1, x, x², x*}, {1, z, z²}, B be ordered bases for Pz and Pz, respectively. Find the matrix [D]E for D relative to the basis B in the domain and C in the codomain. [D]E =

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 17CM
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Let P, be the vector space of all polynomials of degree n or less in the variable z. Let D: P3 + P2 be the linear transformation defined
by D(p(x)) = p'(x). That is, D is the derivative operator. Let
{1, x, x², x*},
{1, z, z²},
B
be ordered bases for Pz and Pz, respectively. Find the matrix [D]E for D relative to the basis B in the domain and C in the codomain.
[D]E =
Transcribed Image Text:Let P, be the vector space of all polynomials of degree n or less in the variable z. Let D: P3 + P2 be the linear transformation defined by D(p(x)) = p'(x). That is, D is the derivative operator. Let {1, x, x², x*}, {1, z, z²}, B be ordered bases for Pz and Pz, respectively. Find the matrix [D]E for D relative to the basis B in the domain and C in the codomain. [D]E =
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