Number of solutions of a system of linear equations

I am looking for MATLAB code to determine the number of solutions (0, 1, Inf) of a system of linear equations (m equations for n variables, e. g.

A=[2,1,3;0, -1,5];
b=[-3;1]
x=A\b

which has infinitely many solutions.

While the answer for the m=n case is given in this excellent post making use of the rank() function I wonder how it can be solved in the general case (m=n, m>n, m<n).

Answer 1

[Dimitris Kalogiros]

Hi Gunther.

You can use solve() within symbolic toolbox.

I'm giving you an example:

syms x y z

eqn1= 2*x + y + 3*z==-3

eqn2= -y + 5*z==1

sol = solve([eqn1, eqn2], [x, y, z], 'ReturnConditions',true);

disp('Solution is :')
[sol.x; sol.y; sol.z]

disp('With parameters : ')
sol.parameters

disp('Under the conditions :')
sol.conditions

Function solve() returns the one solution of the system , or entirely set of solutions if the system has infinite solutions. In case the system has no solutions, sol.x , sol.y , and sol.z are empty.