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Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 43E: Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases...
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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.
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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