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2. Equation Solution using Matrices
Observation equations can be written in the form [C] x [U] = [K]. Using n for the number of unknowns and m for the number of observations, the matirces dimensions are:
_{n}[U]_{1}  _{m}[K]_{1}  _{m}[V]_{1} 
The unknowns in the U matrix are solved using the matrix algorithm Equation D1:
[U] = [C^{T}C]^{1} x [C^{T}K]  
[Q] = [C^{T}C]^{1} 

[U] = [Q] x [C^{T}K]  Equation D1 
[Q] is a symmetric m x m matrix; [C^{T}K] is a m x 1 matrix. Equation D1 is a simultaneous solution of m equations in m unknowns.
Because there are redundant measurements, a residual term is added to each observation equation so the matrix algorithm is [C] x [U] = [K] + [V]. Residuals are computed after the adjustment using Equation D2.
[V] = [CU] [K]  Equation D2 