Stoichiometric coefficient using matrix

%finding the appropriate stoichiometric coefficients for the folowing equation a1FeS + a2O2 = a3FeO + a4SO4

% Fe balance coefficients

Fe=[1 0 -1 0]; S = [1 0 0 -1]; O = [0 2 -1 -1]; b = [0; 0; 0; 0;];

A =[Fe;S;O];

X = A\b;

keep getting the same error code

Error using  \ 
Matrix dimensions must agree.

Error in stoich_1 (line 6)
X = A\b;

[darova]

Matrix A is of 3x4 size. You only have 3 equations for 4 uknown variables

[Ronald Aono]

thanks for the earlier response

%finding the appropriate stoichiometric coefficients for the folowing equation a1FeS + a2O2 = a3FeO + a4SO4

% Fe balance coefficients

Fe=[1 0 -1 0]; S = [1 0 0 -1]; O = [0 2 -1 -1];

A =[Fe;S;O;]; b = [0 0 0 ];

X = A\b'

getting my vector X as zero vector which i know its wrong

stoich_1

X =

0

0

0

0

[Matt J]

It is not wrong. X=zeros(4,1) is a valid solution.

Answer 1

[Jyothis Gireesh]

Since the system of linear equations given above is of the form “Ax = 0”, the solution is given by the basis vectors of the null space of “A”. Any integral multiple of these basis vectors will also be a solution to the above system.

To determine the null space basis vectors, you may use the “null” function in MATLAB. In this case, the solution is given by

x = null(A);

which yields x = [0.5;0.5;0.5] as the result. All the other scaled versions of x will also be a solution.