I am analyzing system of linear equations with coefficients that are part of arithmetic progression.
Example of such system is
I should draw conclusions and prove them for 2x2 and 3x3 systems.
By plotting equation lines it is easy to conclude that all such 2x2 systems have unique solution [-1;2].
By looking at a single equation
I have found that it will evaluate to true if
Does this holds? I would appreciate very much if someone could provide real (rigor) proof.
I have tried few combinations of coefficients in matlab and got [0;-1;2] solution column vector few times, but I also got [NaN; Inf ; -Inf] in some cases. I do not have skills to prove this algebraically, any help?