The linear tranformation L defined by maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases S = L(p(x)) = 9p+5p" E = {r³, r², z, 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) = -10x³ + 5x and g(x) = x² – 13. [L(p(x))] F = [L(g(x))] F =

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 P4 into P3.
(a) Find the matrix representation of L with respect to the ordered bases
S =
L(p(x)) = 9p' + 5p"
E = {x³, 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) = −10x³ + 5x and g(x) = x² – 13.
[L(p(x))] F =
[L(g(x))] F =
Transcribed Image Text:The linear tranformation L defined by maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases S = L(p(x)) = 9p' + 5p" E = {x³, 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) = −10x³ + 5x and g(x) = x² – 13. [L(p(x))] F = [L(g(x))] F =
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