Is this pattern reconstitution or what is the name for this problem?

I've following problem and don't know the terminology to describe it and hence search for possible solutions.

I have a pivot table (matrix), eg each row and column have a named header. there is a defined set for rows and columns. Now let's assume that 1开发者_如何学编程0 rows are "combined" meaning each column is summed up to create a new "pattern". What I would like is a way to determine alternative row combinations that lead to the same or similar "combined" pattern.

1 1 1
5 5 5

"Combined"
6 6 6

alternate row combination:
2 2 2
4 4 4

Suggestions? How is this problem called?

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http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_equation

I just have to transpose above matrix to get Matrix A

[code] 1 5 1 5 1 5 [/code]

combined matrix is a vector b: [code] 6 6 6 [/code]

and x would be just a vector full of 1.