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

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 24CM: Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points...
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The plane z = Ax+By+C is to be "fitted" to the following points (XkYk Zk): (1.0.0), (1.0, -1), (0, -1,-1). (-1,-1,0). Find the values of A, B, and C that minimize
4
Σ (Axk +Byk + C-ZK) 2, the sum of the squares of the deviations.
k=1
A =
3
B =
C =
(Simplify your answers.)
C
Transcribed Image Text:The plane z = Ax+By+C is to be "fitted" to the following points (XkYk Zk): (1.0.0), (1.0, -1), (0, -1,-1). (-1,-1,0). Find the values of A, B, and C that minimize 4 Σ (Axk +Byk + C-ZK) 2, the sum of the squares of the deviations. k=1 A = 3 B = C = (Simplify your answers.) C
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