Let T : P3 → R' be defined by За — 2b + 2с+d | T (ax3 + bæ? + cx + d) а — с — 2d . Let u = r³ – 2, B = {1, x, x² , #³ }, and 2а + с — 2d C = 3 -2 2 1 Given [T -2 -3 -3 ,use the Fundamental Theorem of Matrix Representations to find 1 2 Pe(T(u)). Ex: 5 : Pc(T(u)) =

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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Can I get some help with this "Fundamental Theorem of Matrix Representations" problem?

Let T : P3
be defined by
"За — 2b + 2с +d
T (ax + bæ? + cx + d)
а — с — 2d
. Let u = x – 2, B = {1, x, x² , =³ }, and
2а + с — 2d
C=
3
-2 2
1
Given [T]
-3 -3
, use the Fundamental Theorem of Matrix Representations to find
1
Pe(T(u)).
Ex: 5 :
Pc(T(u))
%3D
Transcribed Image Text:Let T : P3 be defined by "За — 2b + 2с +d T (ax + bæ? + cx + d) а — с — 2d . Let u = x – 2, B = {1, x, x² , =³ }, and 2а + с — 2d C= 3 -2 2 1 Given [T] -3 -3 , use the Fundamental Theorem of Matrix Representations to find 1 Pe(T(u)). Ex: 5 : Pc(T(u)) %3D
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