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Is it a general 4 x 4? If so then why not solve it just once and then plug in from now on.
I meant that it worked well for the 3X3 matrix on paper. The 4X4 matrix was the one that sprawled onto several pages, like you said.
Could you explain a little more what you mean when you say it can be done using Gaussian elimination?
Cramers rule is a horror story. It grows factorially so a 4 x 4 would be awful. Take it over to Wolfram to do the calculations for you. I would not use matlab and or C++ for the job. Or bring them in here and I will do them for you.
I found substitution to be a bit more confusing - I messed it up the last time I tried on paper.
I had understood that the simplex algorithm optimizes a function based on a series of constraints and graphically moves along to get to that optimum. To implement gaussian elimination with the simplex algorithm, would you get rid of the min / max function and then only use equality instead of inequalities for the constraints? I'm not an expert on the simplex algorithm but would like to know.
you need to know about matrix multiplication and also how to construct the inverse matrix, N
** All these methods will 'solve' the equations but you won't necessarily get x = ? y = ? and z = ?
Sometimes a set of equations has no solution and it is even possible to get an infinite number of solutions. But the methods all have a way of showing when this is happening, so you have still got a solution even if it wasn't quite what you were expecting.
There is something simpler. If you insist on solving simultaneous sets of linear equations off course the answers will be very large. No cancelling can occur, no simplification.
It's fairly straight forward to find information on how to solve a system of equations like this: