Solving for unknown parameters in a matrix

[OresteTodini]

I am looking for a way for estimating an unknown parameter in a matrix, so that an equation is satisfied.

I attach an example. In the matrix "alpha" there is an unknown parameter "Par" that I would like to estimate in order to satisfy the equation reported after.

I am using Find, but I cannot estimate only the unknown paramter. The whole matrix is evaluated and actually mathcad changes the alpha 3,3 value, which belongs to the diagonal which must be of 0.

Anyone can help - Thanks a lot in advance

[AlanStevens · Accepted solution]

See attached for a way to structure the solution (and you need to solve for Par, not alpha). However, I think there is probably something wrong with your long expression involving all those summations - it never gets anywhere near zero!!

Alan

Message was edited by: AlanStevens On further investigation it looks to me like you might have got the subscripts the wrong way around on the alpha terms in the summations. A quick way to check is just to transpose alpha where it's defined (and leave the subscripts as they are). You can then put back the 'Find' (and it works even with a poor guess for Par) - see find&matrix3 attached

[OresteTodini]

Alan, thanks a lot - it did work.

I am applying the procedure to a similar problem, but with 3 matrices of parameters and n data points. I have problems with one of the matrix. Any suggestion how to overcome the issue.

The excel file contains the input data for the mathcad sheet.

Thanks a lot in advance, Oreste