2. Linear Maps (a) Let Pn denote the space of polynomial of degree at most n with real coefficients. Find the matrix representation of the differential operator D: P3 → P2 given by D(at³ + bt² + ct + d) = 3at² +2bt + c with respect to the standard monomial basis for P3 and P2. (b) Do the same as above with {2, (t+1)/2, t²} for a basis of the range of D (still use the standard monomial basis for the domain of D).

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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2. Linear Maps
(a) Let Pn denote the space of polynomial of degree at most n with
real coefficients. Find the matrix representation of the differential
operator D : P3 → P2 given by
D(at³ + bt² + ct + d) = 3at² + 2bt + c with respect to the
standard monomial basis for P3 and P2.
(b) Do the same as above with {2, (t + 1)/2, t²} for a basis of the
range of D (still use the standard monomial basis for the domain of
D ).
Transcribed Image Text:2. Linear Maps (a) Let Pn denote the space of polynomial of degree at most n with real coefficients. Find the matrix representation of the differential operator D : P3 → P2 given by D(at³ + bt² + ct + d) = 3at² + 2bt + c with respect to the standard monomial basis for P3 and P2. (b) Do the same as above with {2, (t + 1)/2, t²} for a basis of the range of D (still use the standard monomial basis for the domain of D ).
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