Request explain this example. The mechanism of how LHS gets converted to rows in RHS matrix is not clear Example 6: Check whether or not the map 0:S →GL, (R): 0(0)=P(G),where the i-th row of P(G) is the o(i)-th row of the identity matrix, is arepresentation of S.Solution: To help you understand 0, consider an example when n = 3.010001e((1 2)) = 1 0 0, 0((3 2 1)) = 1 0 0 and (1,2)(3,2,1) = (2,3).001)0101So 0((2,3))= 0 0 1010100) (0 1P(0,0₂) =n0/0 0 11 0 0 1 0 0 =0(12) 0(321) .001 0 1.0In general, you can see that is well-defined, and[0,0₂(1 0...0)0,0₂ (01...0):0,0₂(0 0... 1)= P(o,) P(0₂).representation of S.

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Answered: Example 6: Check whether or not the map…

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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Request explain this example. The mechanism of how LHS gets converted to rows in RHS matrix is not clear

Example 6: Check whether or not the map 0:S →GL, (R): 0(0)=P(G),
where the i-th row of P(G) is the o(i)-th row of the identity matrix, is a
representation of S.
Solution: To help you understand 0, consider an example when n = 3.
010
001
e((1 2)) = 1 0 0, 0((3 2 1)) = 1 0 0 and (1,2)(3,2,1) = (2,3).
001)
010
1
So 0((2,3))= 0 0 1
010
100) (0 1
P(0,0₂) =
n
0/0 0 1
1 0 0 1 0 0 =0(12) 0(321) .
001 0 1.0
In general, you can see that is well-defined, and
[0,0₂(1 0...0)
0,0₂ (01...0)
:
0,0₂(0 0... 1)
= P(o,) P(0₂).
representation of S.

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Not clear . Matrix multiplication part is clear. But initially how does Theta(3 2 1) get converted to the RHS matrix? If in theta (12) we assume third row remains unchanged and row one and two of identity matrix get exchanged, then this logic does not hold goof for Theta (3 2 1). here 001 should appear in second row, 010 in first row and 100 to third.

Request explain the logic of transforming LHS to matrix in RHS

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