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What about the unknow black dot, right in the middle of the following know cells of a very simple 3 x 3 numerical problem?

This problem can be solved numerically, by methods such as in the iterative math’s of a Spreadsheet   ... or it can be addressed by the so-called inverse problem

The inverse problem is a baseline mathematical expedient, where the design matrix, the sensitivity, derivarive (Jacobiam) or just X matrix is used to express the “acction” of all the known variables of a given model. 

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05.3_3x3_Numerical.PNG
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Fonte: Notas de aula, Prof. Luiz Ferrari  IGC - CEPAS|USP
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Covariance matrix
The model is seen here in terms of its Heads ( h ) and ( k ) variables  

Beta μ

The covariance matrix, displays all the possible interconnections within a unique set of data, the 1.1 to 3.3 locations where the model is taking place, actually.

So those intermingled relationships are expressed by the X matrix, oops, ... the Z matrix !
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