The linear tranformation L defined by maps P₁ into P. (a) Find the matrix representation of L with respect to the ordered bases S L(p(x)) 9p -11p" E = {¹, ², 2, 1) and F= {x²+x+1, 2+1,1} (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -4³ -13r and g(x) = x² + 8. [L(p(x))] p= [L(g(x))]=

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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The linear tranformation L defined by
maps P₁ into P3.
(a) Find the matrix representation of L with respect to the ordered bases
S =
L(p(x)) = 9p 11p"
E = {³, z², z, 1} and F = {z²+z+1, z +1,1}
(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) =
) = −47³ - 13x and g(x) = x² + 8.
[L(p(z))] p=
[L(g(x))] F =
Transcribed Image Text:The linear tranformation L defined by maps P₁ into P3. (a) Find the matrix representation of L with respect to the ordered bases S = L(p(x)) = 9p 11p" E = {³, z², z, 1} and F = {z²+z+1, z +1,1} (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = ) = −47³ - 13x and g(x) = x² + 8. [L(p(z))] p= [L(g(x))] F =
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