In the vector space P (polynomial space) consider the linear operators D, A : P+ P defined by D(p(x))=p' (x) A(p(x))=xp(x) a)Find a base for each subspace: Ker (D) and Im (D), Ker (A) and Im (A). b)Determine DA-AD

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Linear  Algebra 

In the vector space P (polynomial space) consider the linear operators
D, A : P+ P
defined by
D(p(x))=p' (x)
A(p(x))=xp(x)
a)Find a base for each subspace: Ker (D) and Im (D), Ker (A) and Im (A).
b)Determine DA-AD
Transcribed Image Text:In the vector space P (polynomial space) consider the linear operators D, A : P+ P defined by D(p(x))=p' (x) A(p(x))=xp(x) a)Find a base for each subspace: Ker (D) and Im (D), Ker (A) and Im (A). b)Determine DA-AD
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