Using the below insights: obtain a matrix P such that if A is any matrix with 3 columns, AP is a cyclic shift of the columns of A (namely the first column of A is the second column of AP, second column of A is the third column of AP, and the third column of A becomes the first column of AP). # Let A = a-1, a-2, ..., a-n # x = x-1, x-2, ..., x-n # Ax = x-1*a-1 + x-2*a-2 + ... + x-n*a-n # [x1] [x1] # A = [x2] = [a1 a2 ... an]* [x2] = a1*x1 + a2*x2 + ... + an*xn # [...] [...] # [xn] [xn]

Using the below insights: obtain a matrix P such that if A is any matrix with 3 columns, AP is a cyclic shift of the columns of A (namely the first column of A is the second column of AP, second column of A is the third column of AP, and the third column of A becomes the first column of AP). # Let A = a-1, a-2, ..., a-n # x = x-1, x-2, ..., x-n # Ax = x-1a-1 + x-2a-2 + ... + x-na-n # [x1] [x1] # A = [x2] = [a1 a2 ... an] [x2] = a1x1 + a2x2 + ... + an*xn # [...] [...] # [xn] [xn]

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section2.5: The Inverse Of A Matrix

Problem 8P

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