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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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2. Consider the bases E = = {1, t, t²} and B = {1+t,t+t², t²} for P2 and the linear transformation
T: P₂ → P₂ defined by T(p(t)) = t p'(t), where p'(t) is the derivative of p(t).
(a) Find the coordinate vector of t² relative to B.
(b)
(c)
Find the change-of-coordinates matrix P from B to E.
E-B
(e)
Find [T], the E-matrix of T.
(d)
We know that the two matrix representations [T] and [T] are similar; that is
[TB = P¹[T]EP for some invertible matrix P. What is P?
What is the kernel of T?

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