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## 3. The Weight Matrix

Equation E-4 is the general matrix algorithm for observation equations with *weight matrix*, **[W]**, included; Equation E-5 is the matrix solution for the unknowns.

Equation E-4 | |

Equation E-5 |

Because each observation has a weight, **[W]** is a diagonal *m *x *m *matrix, Figure E-5.

Figure E-5 Weight Matrix |

The _{i}w_{i} element is the weight for the *i*th observation. Off-diagonal elements are zero.

Since the weight matrix appears on both sides of Equation E-4, it cancels when computing the residuals, Equation E-6.

Equation E-6 |

Weights are used in the standard deviation of the unit weight computation, Equation E-7.

Equation E-7 |