I was wondering if anyone would be able to provide help with a logical method of finding a redundant equation in a system of linear simultaneous equations. By 'redundant', I mean that I want to be able to find an equation which could be removed without preventing solutions from being found to the system of equations.
For example, if the system states that 'a=1 and b=2' then neither equation is redundant because information is lost by removing either equation. However, if the system states that 'a=b-1, a=1, and b=2' then any one (but not more than one) of these equations could be removed without any information being lost. Another example of a system with redundant equations would be if 'a=b, a=2, b=2, c=1, and d=c'. I could remove any one (but not more than one) of the first three without losing any information, but neither of the last two equations can be removed.
The reason that I want a way to find the redundant equations is because I am making a program that will convert chemical equations into a system of simultaneous equations, then will solve the simultaneous equations and use the solutions to balance the original chemical equation. The function that I have made that solves the simultaneous equations does not work if there are any redundant equations, which is why I need a logical method for how to fnd any redundant equations, as I will make the computer remove a redundant equation before solving. The user cannot just change the way that they type in the chemical equation, because that would defy the laws of chemistry.
Thank-you in advance.