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The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1), (1,-1,-1), (0,0,-1). Find the values of A, B, 4 and C that minimize Σ (AxK+Byk + C-ZK) ², the sum of the squares of the deviations. k=1 A = B = C = (Simplify your answers.)

The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1), (1,-1,-1), (0,0,-1). Find the values of A, B, 4 and C that minimize Σ (AxK+Byk + C-ZK) ², the sum of the squares of the deviations. k=1 A = B = C = (Simplify your answers.)

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 10E
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The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (− 1, −1,1), (1,-1,-1), (0,0,1). Find the values of A, B, 4 and C that minimize Σ (AxK+Byk + C-ZK) ², the sum of the squares of the deviations. k=1 A = B = C = (Simplify your answers.)
Transcribed Image Text:The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (− 1, −1,1), (1,-1,-1), (0,0,1). Find the values of A, B, 4 and C that minimize Σ (AxK+Byk + C-ZK) ², the sum of the squares of the deviations. k=1 A = B = C = (Simplify your answers.)
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