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- Let T : Pn → Pn-1 be T(p) = dr. Find its range and dx nullspace (with explanations) and hence its rank and nullity (Hint: Basic calculus).

- Let T : Pn → Pn-1 be T(p) = dr. Find its range and dx nullspace (with explanations) and hence its rank and nullity (Hint: Basic calculus).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let T PnPn-1 be T(p) dp Find its range and dx nullspace (with explanations) and hence its rank and nullity (Hint: Basic calculus). = - Let T: Pn → Pn+1 be T(p) = xp(x). Find its range and nullspace (with explanations) and hence its rank and nullity (Hint: The range of T is not all of Pn+1 - what is certainly one root of xp(x)? For the rank and nullity you may invoke the rank-nullity theorem.)
Transcribed Image Text:Let T PnPn-1 be T(p) dp Find its range and dx nullspace (with explanations) and hence its rank and nullity (Hint: Basic calculus). = - Let T: Pn → Pn+1 be T(p) = xp(x). Find its range and nullspace (with explanations) and hence its rank and nullity (Hint: The range of T is not all of Pn+1 - what is certainly one root of xp(x)? For the rank and nullity you may invoke the rank-nullity theorem.)
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