Solving linear matrix equation

Hi. I want to slove a linear matrix equation AX=B by this code : X=A\B When i run this code it will show me the solved X matrix. But i can not understand that which value is for which variable. It just show me the X matrix without showing the name of each variable.i had defined my variables by sym. And there are too many variables that i can not name them one by one in the code.for example , There are variables ,for example x y z ... in my equations. How can i understand which cell of X matrix us the value of x or y or z?! Please help me!!

[Stephen23]

@Amir hossein Abrishamkar: you are using the wrong operator: to solve equations with the form A*x=B you need to use mldivide, not mrdivide.

[Torsten]

X=A\B, not X=A/B.

And what name should be shown ? X is a matrix, and the elements of X can be addressed as X(1,1), X(2,1),... . If you want to express it this way: the position (i,j) within the matrix X is the name of the corresponding variables.

Best wishes

Torsten.

[Amir hossein Abrishamkar]

Dear @torsten. There are variables for example x y z ... in my equations. How can i understand which cell of X matrix us the value of x or y or z?!

[Torsten]

It's the same order in which you defined the "vars" vector in the call to "equationsToMatrix".

[Amir hossein Abrishamkar]

@torsten. But i had not defined vars matrix in equationstomatrix. I had only defined vars by "sym" and just made equations by these vars and called equations to equationstomatrix.

[Torsten]

Then it should be in alphabetic order of the symbolic variables used, I guess. Test it.

But I'd recommend to prescribe the order yourself by supplying a "vars" vector.

Answer 1

[John D'Errico]

I think you do not understand how MATLAB works, how it returns results? Perhaps you have only used other tools like Excel or Mathematics, that will often show results somewhat differently.

When you write this:

A = rand(5,5);
B = rand(5,1);

X = A\B;

MATLAB returns the result in a vector X.

X =
   -0.84086
     3.7698
     3.8571
    -8.0047
     2.4444

But MATLAB does not name the individual components of the vector. They are simply

X(1), X(2), X(3), ...

That is the "name" associated with an element of a vector (or an array). Thus we can extract an element as:

X(1)
ans =
   -0.84086

If you really felt you needed named variables, you could have used the symbolic toolbox, formulating a linear system of equations in those variables, then solving the system. The result would have had named variables containing the desired values. But it really is not necessary here, and it would be much more slowly computed in symbolic form. Essentially, that would be vast overkill for a simple problem.

[Amir hossein Abrishamkar]

I had formulated a system of equations by named variables such as x y z ... . Then i had changed this system to matrix by equationstomatrix function. Now i want to solve this matrix equation and i wish to know that which value of X matrix is for the my named variable such az y or z! There is no way to understand that?? Thanks alot for your answers!

[John D'Errico]

So read the help for equationstomatrix. You apparently told it to create a matrix using a call something like this:

A = equationsToMatrix([eq1,eq2,eq3],[x,y,z])

The you solved the problem using linear algebra, thus backslash. In the solution, X(1) will be synonymous with x. X(2) will be synonymous with y.

But as far as backslash is concerned, the names x,y,z are irrelevant. It does not see them. It was posed a pure matrix problem, solved as such. Backslash solved for a vector of solutions. Only you know of the synonymous relationship. Nothing stops you from writing this:

x = X(1);
y = X(2);
Z = X(3);

Although you could do it in more tricky ways.

If you used equations to matrix like this:

A = equationsToMatrix([eq1,eq2,eq3])

Well, then your results are worth just the amount of effort you put into them - essentially nothing. You are then left with having to guess which order the variables were implicitly used. Can I suggest this was a REALLY bad idea? While it MAY be true that the variables are in some variation of alphabetical order, that is not at all a given. (In fact, I had just this discussion two days ago with a rather well-known MathWorks founder. The order they will be used is probably not alphabetical.)

Had you used this call form instead, there would be no ambiguity:

A = equationsToMatrix([eq1,eq2,eq3],[x,y,z]);

[Amir hossein Abrishamkar]

But my variables are arrays from a matrix!! And also there are some zero arrays in that matrix. How can i mention that variable array in equationstomatrix?

[John D'Errico]

Sorry, but you make no sense in context of this discussion: "my variables are arrays from a matrix". And what do the presence of some zeros have to do with anything? Zeros are just a number.

You have some unknowns that you wish to solve for. Why not just use solve? Let me guess. You have either more or fewer unknowns than equations. So solve found no solution, for good reason. Either there are no solutions at all, or there are infinitely many solutions.

I think a big problem in this question is that I am trying to chase a moving target. Every time you get an answer, the question changes, and you reveal some additional aspect of some totally different and hidden question.

If you insist on using equationstomatrix, then you need to learn how to use it properly. The problem is not with the solve. You need to formulate the problem properly, as otherwise you will get random garbage from any solver. But we are still peeking around corners at the problem, not being told the entire problem.

So go back to equationstomatrix. Learn to use it, and to use it properly. Verify that the matrix it produces is one that makes sense, and where the variables are known. Only then should you try to solve anything.