(c) Calculate the matrix representing T with respect to the standard basis e₁ = (1,0)¹, e₂ = (0, 1) of R² and the basis {V₁, V2, V3, V4, V5} of P₁ (R).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let T: P₁ (R) →→ R2 be the map given by
T(S) = (S(1).J" (1))
where P₁ (R) is the set of polynomials of degree 4 or less and f" (1) is the evaluation of
d³ f
the third derivative of f at 1, i.e.,
dx³ x=1
Transcribed Image Text:Let T: P₁ (R) →→ R2 be the map given by T(S) = (S(1).J" (1)) where P₁ (R) is the set of polynomials of degree 4 or less and f" (1) is the evaluation of d³ f the third derivative of f at 1, i.e., dx³ x=1
(c) Calculate the matrix representing T with respect to the standard basis e₁ = (1,0)¹,
e₂ = (0, 1) of R² and the basis {V₁, V2, V3, V4, V5} of P₁ (R).
Transcribed Image Text:(c) Calculate the matrix representing T with respect to the standard basis e₁ = (1,0)¹, e₂ = (0, 1) of R² and the basis {V₁, V2, V3, V4, V5} of P₁ (R).
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