The linear tranformation L defined byL(p(x)) = 3p' – 10p"maps P4 into P.(a) Find the matrix representation of L with respect to the ordered basesE = {x°, x², x, 1} and F = {x² + x +1, x + 1, 1}(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = –3x12х and g(a) — а? — 5.= -.[L(p(x})]r = (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -3x³- 12x and g(x) = x² – 5.[L(p(x)))F=[L(g(x))]F=

We have to find the following given conditions according to the given information

Answered: nformation L defined by L(p(x)) = 3p' –…

nformation L defined by L(p(x)) = 3p' – 10p" P3. natrix representation of L with respect to the ordered bases E = {r°, x², x, 1} and F = {x² + x + 1, æ + 1, 1}

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 38EQ

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Question

The linear tranformation L defined by
L(p(x)) = 3p' – 10p"
maps P4 into P.
(a) Find the matrix representation of L with respect to the ordered bases
E = {x°, x², x, 1} and F = {x² + x +1, x + 1, 1}
(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = –3x
12х and g(a) — а? — 5.
= -.
[L(p(x})]r =

(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -3x³
- 12x and g(x) = x² – 5.
[L(p(x)))F=
[L(g(x))]F=

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