Solve Command with Matrix

[Heavenly]

At the bottom of the attached sheet I am trying to solve for lengths YD and ZD that will work for all three equations simultaneously. It is telling me ZD is undefined. Is this because there is no solution or that I am doing something incorrectly with the solve block and the matrix guess values? Any help is appreciated. Thanks. The file is MathCAD 15.

[Werner_E]

I did not have a close look at you sheet, but this is what I get when I use error tracing (right click on the offending red ZD)

and if I check I see that Mathcad is perfectly right:

If I repair the situation by adding an additional value to the vectors of guess values, I get the "no solutions found" error

Be aware that a solve block will always only throws the "variable undefined" error, no matter whats really the cause. You can only get more information via error trace.

The problem seems to be, that you have three equations but only two variables to solve for. This system of equations might be unsolvable.

Disabling any of the three equations gives you a solution, but there is no solution if you insist an all three equations.

[Werner_E]

After correcting the length of the guess vectors - here is an approach using minerr. Not sure if an aberration of   approx 4,9 % in case of I.x would be tolerable. The other deviations are quite moderate - less than 1%.

[Heavenly]

Thanks Werner!

[Heavenly]

Werner,

Another question for you. How do you create a submatrix which the mean of every two rows in the matrix YD? Example (9.91+9.98)/2, (9.98+10.05)/2,(10.05+10.12)/2, etc.