system of linear equations with unorganized unknowns

Hi everybody

First, I want to apologize if my question is answered already, but I couldn't find proper easy answer.

I have system of equation formed as [k]*[u]=[f] in which [k] is known and [u] and [f] have known and unknown variables. the matrix [k] is n by n and [f], [u] are n by 1 matrixes. I want to know what is the simplest way to solve this system of equation?

I am beginner in MATLAB and thanks in advance.

[darova]

Are number of uknowns and number of equations equal?

[Kasra Shamsaei]

Yes they are equal

[darova]

Try equationsToMatrix if the system is linear

Try fsolve if it's not

[Kasra Shamsaei]

The system is linear but the problem is that the eqntomatrix command converts equations to matrix But the problem is that I don’t have the equations to convert. I have the matrix form of equations as I said before with unknowns on both sides.

Answer 1

[darova]

Here you go

u = sym('u',[10 1]);
f = sym('f',[10 1]);
f([2 4 6]) = 1;         % constants
u([1 3 5 7:10]) = 1;    % constants
k = rand(10);           % coefficinet matrix
eqns = k*u-f;           % symbolic equations
vars = symvar(eqns);    % get all unknown variables
[A,B] = equationsToMatrix(eqns,vars);
A = double(A);
B = double(B);
res = A\B;
str = arrayfun(@char, vars, 'uniform', 0)';
table(str,res)

Answer 2

[Ameer Hamza]

In most cases, if your matrix k is general, then the most efficient way is

u = k\f;

The above method is also recommended by MATLAB's documentation. But if matrix 'k' has some special properties such as it is a triangular matrix, then linsolve can give speed gain: https://www.mathworks.com/help/releases/R2020a/matlab/ref/linsolve.html#mw_f405bef0-76ac-4c5b-8c40-c65d1a0a331e.