Replace values in a matrix with minimums for ranges based on a separate same size matrix in Mathcad.

This request is more fully explained in the attached file. The request is for a way to take two single column vectors or matrices that are effectively two columns of a table when augmented (i.e., namely matrix A and matrix B). The first matrix "A" has several rows that have repeated values. A function has been run to create a new matrix "C" that has removed the duplicate rows.

Please help to write a function that will create matrix "D" such that "D" contains the minimum values from the second matrix "B" pertaining to rows that had the same value in matrix A. Thus, matrix D ensures that removal of duplicate rows from A does not lose the minimum associated values in "B". I think the details in the attached Mathcad Prime 10 file will help clarify this request.