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Find the least squares solution of the n linear equations ax + b₁y = ci i=1,2,...,n, where ab; - abi #0 for i # j. If rj, j = 1,2,..., k = n(n-1)/2 are the solutions of all possible pairs of such equations, show that the least squares solution --( ;) is a convex linear combination of rj, specifically where T = ΣPjTj, j=1 P₁ = D} Σ - D and D, is the determinant of the jth 2-equation subsystem. Interpret this result geometrically.

Find the least squares solution of the n linear equations ax + b₁y = ci i=1,2,...,n, where ab; - abi #0 for i # j. If rj, j = 1,2,..., k = n(n-1)/2 are the solutions of all possible pairs of such equations, show that the least squares solution --( ;) is a convex linear combination of rj, specifically where T = ΣPjTj, j=1 P₁ = D} Σ - D and D, is the determinant of the jth 2-equation subsystem. Interpret this result geometrically.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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11. Find the least squares solution of the n linear equations aix + b₁y = ci i=1,2,...,n, where abajbi #0 for i # j. If rj, j = 1,2,..., k = n(n-1)/2 are the solutions of all possible pairs of such equations, show that the least squares solution r = ( ;) is a convex linear combination of rj, specifically where -ΣPjTj, j=1 T = D Pj Σ= D and D, is the determinant of the jth 2-equation subsystem. Interpret this result geometrically.
Transcribed Image Text:11. Find the least squares solution of the n linear equations aix + b₁y = ci i=1,2,...,n, where abajbi #0 for i # j. If rj, j = 1,2,..., k = n(n-1)/2 are the solutions of all possible pairs of such equations, show that the least squares solution r = ( ;) is a convex linear combination of rj, specifically where -ΣPjTj, j=1 T = D Pj Σ= D and D, is the determinant of the jth 2-equation subsystem. Interpret this result geometrically.
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