given a square matrix a with n columns and a vertical vector b where rank(a)=rank(a|b)<n, solve the system ax=b in matlab

To solve the system ax = b in MATLAB, where a is a square matrix with n columns and b is a vertical vector, you can use the built-in MATLAB function linsolve.

First, make sure that the rank of a is equal to the rank of [a, b]. If they are not equal, it means that the system is inconsistent and does not have a solution. You can check this using the rank function in MATLAB.

Here is an example code that solves the system ax = b:

main.m
% Input matrix and vector
a = [1, 2, 3; 4, 5, 6; 7, 8, 9];
b = [10; 20; 30];

% Check that the ranks are equal
if rank(a) ~= rank([a, b])
    disp('The system is inconsistent and does not have a solution.');
    return;
end

% Solve the system
x = linsolve(a, b);

% Display the solution
disp('The solution is:');
disp(x);
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Make sure to replace the values of a and b with your actual matrix and vector.

Note that linsolve can also be replaced with the backslash operator (\) in MATLAB, which is usually more efficient for solving systems of linear equations. You can use x = a \ b; instead of x = linsolve(a, b);.