## Finding a Solution to a Set of Equations in Mathcad

Firstly, let’s consider a set of linear algebraic equations in Mathcad. In order to find a solution to the equations a unit given …find() or a special function lsolve() can be used. Application of unit given …find() predetermines the necessity of assigning the initial values of the desired variables. Later, after the key word given, a set of linear algebraic equations is generated and the find() helps to find the solution. It should be mentioned that in case the set of linear algebraic equations in Mathcad has an infinite set of solutions, case given …find() offers a concrete result, which is definitely a shortcoming. In case of absence of any solution, a message “Matrix is singular. Cannot compute its inversу” comes on screen.

Function lsolve( ) can help to avoid the mentioned above shortcoming. Function lsolve(M,b) has two arguments. M – is the matrix of coefficients which determine the unknown variables, b – is vector of absolute terms. The programme listing shows the example of finding a solution to such a set of linear algebraic equations.

Example: In order to find a solution to the set of nonlinear equations two units are in use: given…find() and given…minerr (). As a set of nonlinear equations can have several solutions, the obtained results depend on the initial values of desired variables. In both cases we get approximate solutions, which require solution check. Normally it is required in Mathcad that the number of equations is equal to the number of the desired variables, but in some cases, when from the point of view of classical mathematics a correct solution can be found with a smaller number of equations, this condition can be neglected. The programme listing shows the examples of units given…find() and given…minerr () in use in order to find solution to sets of nonlinear equations. 