dp(x) Let T : P2 → P4 be the linear transformation given by T(p(x)) : - 2.xp(x)+ 3P(x²). dx where P2, P3 are the spaces of polynomial of degree at most 2 and 3 respectively. (a) Find the matrix representation of T relative to the bases {1, x, x²} for P2. (b) Find the kernel of T.
dp(x) Let T : P2 → P4 be the linear transformation given by T(p(x)) : - 2.xp(x)+ 3P(x²). dx where P2, P3 are the spaces of polynomial of degree at most 2 and 3 respectively. (a) Find the matrix representation of T relative to the bases {1, x, x²} for P2. (b) Find the kernel of T.
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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Need help with a and b
Transcribed Image Text:dp(x)
Let T : P2 → P4 be the linear transformation given by T(p(x)) =
where p2, P3 are the spaces of polynomial of degree at most 2 and 3 respectively.
— 2лгp (т) + ЗP(?).
dx
(a) Find the matrix representation of T relative to the bases {1,x, x²} for P2.
(b) Find the kernel of T.
(c) Find a basis for the range of T.
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