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 8((1 2)) = 100, ((3 2 1))= 1 0 0 and (1,2)(3, 2, 1) = (2,3). 0 0 1 0 1 0) 100 So 0((2,3))= 0 0 1 0 0 = P(0,0₂) = →>> (0 1 0 (00 100 00 : 0,0₂(0 0... 1) In general, you can see that is well-defined, and [0,0₂(1 0...0) 0,0₂(01...0) 100 =0(12) 0(3 21). 0 1.0)
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 8((1 2)) = 100, ((3 2 1))= 1 0 0 and (1,2)(3, 2, 1) = (2,3). 0 0 1 0 1 0) 100 So 0((2,3))= 0 0 1 0 0 = P(0,0₂) = →>> (0 1 0 (00 100 00 : 0,0₂(0 0... 1) In general, you can see that is well-defined, and [0,0₂(1 0...0) 0,0₂(01...0) 100 =0(12) 0(3 21). 0 1.0)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 15CR
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Request explain this example. The mechanism of how LHS gets converted to rows in RHS matrix is not clear
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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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