Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space of polynomials of degree < 2. (a) Find the transition matrix, P from B to E. E-B (b) Find the transition matrix, P from & to B. B-E (c) Find the coordinate vector, [p(t)]B, of p(t) = 1+t+ť² relative to B. Page 2 of 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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There are 4 parts to the question. 2a, 2b, 2c, and 2d.

(d) Find the E-matrix of the linear transformation T: P₂ → P2, T(p(t)) = p'(t) + 2p(t).
Transcribed Image Text:(d) Find the E-matrix of the linear transformation T: P₂ → P2, T(p(t)) = p'(t) + 2p(t).
Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space
of polynomials of degree < 2.
(a) Find the transition matrix, P from B to E.
E-B
(b) Find the transition matrix, P from & to B.
B-E
(c) Find the coordinate vector, [p(t)]B, of p(t) = 1+t+ť² relative to B.
Page 2 of 2
Transcribed Image Text:Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space of polynomials of degree < 2. (a) Find the transition matrix, P from B to E. E-B (b) Find the transition matrix, P from & to B. B-E (c) Find the coordinate vector, [p(t)]B, of p(t) = 1+t+ť² relative to B. Page 2 of 2
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Please answer only part d. 

(d) Find the E-matrix of the linear transformation T: P₂ → P2, T(p(t)) = p'(t) + 2p(t).
Transcribed Image Text:(d) Find the E-matrix of the linear transformation T: P₂ → P2, T(p(t)) = p'(t) + 2p(t).
Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space
of polynomials of degree < 2.
(a) Find the transition matrix, P from B to E.
E-B
(b) Find the transition matrix, P from & to B.
B-E
(c) Find the coordinate vector, [p(t)]B, of p(t) = 1+t+ť² relative to B.
Page 2 of 2
Transcribed Image Text:Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space of polynomials of degree < 2. (a) Find the transition matrix, P from B to E. E-B (b) Find the transition matrix, P from & to B. B-E (c) Find the coordinate vector, [p(t)]B, of p(t) = 1+t+ť² relative to B. Page 2 of 2
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