Let s = {1, 2, 3} andT: Fun(S) + R' be the transformation T) = (10), s) – 2/), 1() – 12) and consider the ordered bases E = {X1. X2, xa the standard basis of Fun(S) %3D F = {x1 + x2, xa - x2a, x1 - xa) a basis of source Fun(S) IX EX E' = {(1,0,0), (0,1,0), (0,0,1)} the standard basis of R G= {(-1,-1,1), (1,2,0), (0,1,0)} a basis of target IR Calculate the matrix M(T) representing T relative to input basis Band output basis C for the bases below: ME (T) -2 1. -1 1 ME (T) -3 2 2 -1 MG(T) - ME(T) =
Let s = {1, 2, 3} andT: Fun(S) + R' be the transformation T) = (10), s) – 2/), 1() – 12) and consider the ordered bases E = {X1. X2, xa the standard basis of Fun(S) %3D F = {x1 + x2, xa - x2a, x1 - xa) a basis of source Fun(S) IX EX E' = {(1,0,0), (0,1,0), (0,0,1)} the standard basis of R G= {(-1,-1,1), (1,2,0), (0,1,0)} a basis of target IR Calculate the matrix M(T) representing T relative to input basis Band output basis C for the bases below: ME (T) -2 1. -1 1 ME (T) -3 2 2 -1 MG(T) - ME(T) =
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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Question
![Let s = {1, 2, 3} and T : Fun(S) +R' be the transformation
T) = (10), se) – 2/), (9) – (2)
and consider the ordered bases
E = {X1. X2, xa the standard basis of Fun(S)
F = {x1 + x2, xa - xa, xI - xa) a basis of source Fun(S)
E' = {(1,0,0), (0,1,0), (0,0,1)} the standard basis of R
G = {(-1,-1,1), (1,2,0). (0,1,0)} a basis of target IR
%3D
Calculate the matrix M(T) representing T relative to input basis Band output basis C for the bases below:
ME (T)
-2
1.
-1
1
ME (T)
-3
2
2
-1
MG(T) -
MG(T) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c9bda6b-973d-4fed-91dd-23d2428d0338%2F2aadcdd3-ac9b-493c-9465-7091b81b3cda%2F57u72e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let s = {1, 2, 3} and T : Fun(S) +R' be the transformation
T) = (10), se) – 2/), (9) – (2)
and consider the ordered bases
E = {X1. X2, xa the standard basis of Fun(S)
F = {x1 + x2, xa - xa, xI - xa) a basis of source Fun(S)
E' = {(1,0,0), (0,1,0), (0,0,1)} the standard basis of R
G = {(-1,-1,1), (1,2,0). (0,1,0)} a basis of target IR
%3D
Calculate the matrix M(T) representing T relative to input basis Band output basis C for the bases below:
ME (T)
-2
1.
-1
1
ME (T)
-3
2
2
-1
MG(T) -
MG(T) =
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