(3) (*) Let M2(F) be the set of 2 x 2 matrices with entries in F and let= {p € F[t] |p= 0 or deg(p) < 2}.Consider the linear transformation T : M2(F) F[t]2 defined byFt]2a bTс de al = (a + b) + (2d)t + bt².Compute the matrix of T with respect to the ordered basesB =and C = 1, t, t².

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(3) (*) Let M2(F) be the set of 2 x 2 matrices with entries in F and let F[t]2 = {p € F[t]|p = 0 or deg(p) < 2}. Consider the linear transformation T: M2(F) → F[t]2 defined by a T a = (a + b) + (2d)t + bt². C Compute the matrix of T with respect to the ordered bases [1 0] [o 1] 0 0 0 0 and C = 1,t, t². 1 0

(3) (*) Let M2(F) be the set of 2 x 2 matrices with entries in F and let F[t]2 = {p € F[t]|p = 0 or deg(p) < 2}. Consider the linear transformation T: M2(F) → F[t]2 defined by a T a = (a + b) + (2d)t + bt². C Compute the matrix of T with respect to the ordered bases [1 0] [o 1] 0 0 0 0 and C = 1,t, t². 1 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(3) (*) Let M2(F) be the set of 2 x 2 matrices with entries in F and let
= {p € F[t] |p= 0 or deg(p) < 2}.
Consider the linear transformation T : M2(F) F[t]2 defined by
Ft]2
a b
T
с d
e al = (a + b) + (2d)t + bt².
Compute the matrix of T with respect to the ordered bases
B =
and C = 1, t, t².

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