3. Let P, be the vector space of polynomials of degree at most 2. Define a map D : P2 → P, it sends a polynomial to its derivative. (a) Show that D is linear. (b) Find the matrix of D with respect to the basis {1 – z,1+ 3r², 2+ z – r*}.
3. Let P, be the vector space of polynomials of degree at most 2. Define a map D : P2 → P, it sends a polynomial to its derivative. (a) Show that D is linear. (b) Find the matrix of D with respect to the basis {1 – z,1+ 3r², 2+ z – r*}.
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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Please solve the attachment in typefont and define P2 as ax^2 + bx + c and D as 2ax + b in your solution. Thank you!
Transcribed Image Text:3. Let P, be the vector space of polynomials of degree at most 2. Define a map D : P2 → P, it sends a
polynomial to its derivative.
(a) Show that D is linear.
(b) Find the matrix of D with respect to the basis {1 – z,1+ 3r², 2+ z – r*}.
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