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Just to add more to the mix we can rearrange the equation as x=A^{-1}b. How does this relate to the reduced row echelon form and the identity matrix?

Who understands the matrix equation Ax=b?

To some this may sound like a trivial question. Others won't know what I am talking about. This is the crux of a problem with physics forums. If you don't know the answer and simply come to a forum such as this to have questions answered then I can see no problem with that. That is a learning exercise. If you don't know the answer and you are trying to postulate a new 'theory' to revolutionize physics then you have real problems with your understanding of the subject. You could always google it of course but you may miss the subtleties.

I am trying to fathom why you asked a question to which you obviously know the answer. The manipulation of matrix equations is obviously critical to the understanding of the mathematics of advanced physics, but so is advanced calculus and three dimensional geometry. Now some of us non physicists in trying to understand the status quo get lost in the maths either through lack of knowledge or in my case lack of practise. Its many years since I was required to do it. Some of us have ideas that seem to us OK, but we need you to tell us why they are not. Some of us have tried to study the basics as much as possible (in my case even buying expensive text books), but much of it is statement of fact, rather than how that fact was established. So theories ( or more correctly hunches) inevitably follow.They are of course wrong, but why? It really comes down to what you see is the purpose of the forum. If it for professionals to exchange ideas. Then so be it, there is no point in me or other 'crackpots' contributing. If it is to promote alternatives, there is no point in professionals contributing. I believe it is neither of the above and that it should be an opportunity for interchange between both groups. It is easier to get a date with David Cameron than find a physicist to discuss any ideas you may have. I find the concept of needing to pass the matrix exam before you can discuss physics in a meaningful way a little bit upsetting and may actually prevent future questions through fear of embarrassment. Do you think we should only ask questions of a controversial nature to which we know the answer?

Quote from: jeffreyH on 16/01/2016 16:58:48To some this may sound like a trivial question. Others won't know what I am talking about. This is the crux of a problem with physics forums. If you don't know the answer and simply come to a forum such as this to have questions answered then I can see no problem with that. That is a learning exercise. If you don't know the answer and you are trying to postulate a new 'theory' to revolutionize physics then you have real problems with your understanding of the subject. You could always google it of course but you may miss the subtleties.I searched for this, I have no idea of what it means or what it is trying to explain, I have never learnt this so can not make any sort of assumptions, it says that A = 3*3 xyz. I have no idea what that suppose to mean to start with, to me it means nothing, you cant have 3*3 xyzp.s and not knowing this is not relative to any idea. science keeps doing this , and never listens, that is the problem. Science is not the ''gods'' of thought, ''we'' can think just as well .

Physics is a fascinating subject. As things become clearer it also becomes apparent just how little we actually know. Does that give us a licence to indulge in wild and uninformed speculation? You may say yes. Well if that had always been the case then we would still be living in a fifteenth century society.

The A in the equation is an m by n matrix with m rows and n columns. The x is a vector with n rows and 1 column.The resulting b is also a vector with m rows and 1 column. This means that the two vectors x and b may not be of the same dimension. They will be if matrix A is a square matrix so that m = n but not if this matrix is rectangular so that m <> n. Nowhere does it state that the matrix A has to be 3 rows by 3 columns.

Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.

Quote from: dhjdhj on 17/01/2016 16:36:51Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.I'm glad we sorted that out then.

Quote from: jeffreyH on 17/01/2016 16:20:03The A in the equation is an m by n matrix with m rows and n columns. The x is a vector with n rows and 1 column.The resulting b is also a vector with m rows and 1 column. This means that the two vectors x and b may not be of the same dimension. They will be if matrix A is a square matrix so that m = n but not if this matrix is rectangular so that m <> n. Nowhere does it state that the matrix A has to be 3 rows by 3 columns.arrr, ok, I now understand, yes I now understand it is easy, similar to my poker idea. You have a 3 dimension cube matrix, XYZ, at each point in the matrix there is a variable, does this sound about right for the Matrix you are talking about?So A is area and X is a piece of paper stacked on a piece of paper and so on?

OK. Say we have 3 equations2x + y - 4z = 34x + 5y - z = -6 3y - 3z = 50

If all you have is a hammer everything looks like a nail. If all you have is the description of a hammer how do you even know what a nail is?

I think there may more of a grain of truth in Timey's post . Mathematics may have become the primary partner in the marriage with concept. Dirac took the view that structure didn't matter as long as the maths was correct. I can't reconcile myself to that view. Even the fact that Heisenberg and Schrodinger ended up with compatible maths from different concepts gives me pause for thought. From what I have read there have been notable physicists who were not good at maths. Faraday for a start. Of course if the maths is wrong, the idea cant be right ,but if the maths is right it does not necessarily mean the idea is right. I take it Jeffrey you want some one specific to solve your problem.

A hammer is a tool, and so is a nail. Play with your tools all you like, they are fun I must admit, but if you are to use your tools to build a representation of the universe, it is necessary to refer back to reality.The reality is that the tools haven't quite been able to fully represent the reality, so why are you blowing a trumpet over the tools?

I think you have made your point Jeffrey

You are missing the point entirely. If you are fixing trucks you need particular tools. You could try just using any old thing. You could try a chainsaw to get the wheels off, or the exhaust etc etc. However it is required to use the tools of the trade. The problem with the mathematics of physics is not that it is fuzzy and bodged together but that the language used and the terms involved are understood by an exclusive set of individuals. However the same is true of the parts on a vehicle. Unusual names should not be a reason to rubbish the tools of the trade. It just means a shallow learning curve. (yes that does mean difficult unlike the misused steep learning curve.) That is no reason to avoid the learning process altogether.

You are missing the point entirely. If you are fixing trucks you need particular tools. You could try just using any old thing. I don't think I am. I absolutely agree that you need the tools and the skills to use them and maths is a tool to help understand physics, but to use your analogy if you fixing trucks the tools are determined by the job, you don't change the job to suit the tools. In my own experience as a young engineer I was required to plan the design and construction of complex projects with multiple resources and numerous uncertainties. We used many of the same mathematical tools that Physicists use, as well as creating some of our own, but the whole purpose was to get the job done our only output was progress. I don't people find the maths is so much of a barrier as the language of physics. You may have noticed I deliberately avoid this language where ever possible because it has to so precise and even physicists writing popular science books can get it wrong. My point is that maths is vital to understanding existing theories and vital to confirming new ones but surely it can not be a substitute for thought as to what is actually happening.

Physics is a creative process. But you have to be able to take the idea that has been created and test it rigorously. I have nothing against creativity in physics but please don't expect others to finish off the job. If you can't take your own idea further then that is your problem. Why should anyone give up their time and take it away from time with family or friends on a whim? Criticism is one thing but investment of time is another.

The solution to the problem isx = -13.145y = 7.495z = -9.205Go here ...sorry, you cannot view external links. To see them, please REGISTER or LOGINType the following with spaces into the matrix text area and click matrix inverse and then calculate2 1 -44 5 -10 3 3You should then get a new matrix with the values:-0.750 0.625 -0.792 0.500 -0.250 0.583-0.500 0.250 -0.250Copy this then click on back to online matrix calculator and then click the link matrix multiplication.Copy the results matrix into the matrix a box then type the following into the matrix b box3-650Then click multiply A*B. You will then get the solution for x, y and z.

I could go through it step by step but I won't. Google row echelon form and do a bit of reading. You might actually learn something.

Jeffrey I think you are referring to my idea/hypothesis/hunch and you are right I am a bit stuck, and I would like some help, but only IF the idea is worth pursuing. Now unlike timey I have no paranoia, I am a retiree with a good life style. I don't need any fame or fortune. What I do need is someone to tell me what's wrong so I can either work round it or move on. Now if you are saying that what I have proposed contains no obvious violations of basic physics, but needs mathematical validation either positive or negative then that's a whole new ball game. Mathematicians I can find. Physicists are like hen's teeth, good ones even rarer.

Well then there you go. Julian Barbour agrees with you, but not many others

Quote from: jeffreyH on 17/01/2016 19:05:50The solution to the problem isx = -13.145y = 7.495z = -9.205Go here ...sorry, you cannot view external links. To see them, please REGISTER or LOGINType the following with spaces into the matrix text area and click matrix inverse and then calculate2 1 -44 5 -10 3 3You should then get a new matrix with the values:-0.750 0.625 -0.792 0.500 -0.250 0.583-0.500 0.250 -0.250Copy this then click on back to online matrix calculator and then click the link matrix multiplication.Copy the results matrix into the matrix a box then type the following into the matrix b box3-650Then click multiply A*B. You will then get the solution for x, y and z.Using a calculator is cheating and I still have no idea of what it is trying to show or represent?

It was your reference to money and people stealing ideas. If I got the wrong end of the stick I apologise.