pseudoinverse method to solve overdetermined system of equations in matlab

To solve an overdetermined system of equations in MATLAB, one can use the pseudoinverse method. The pseudoinverse is a generalization of the matrix inverse for nonsquare matrices.

Assuming we have a system of equations with matrix A and vector b such that Ax = b. If A has more rows than columns, then the system is overdetermined (more equations than variables). In this case, the solution x that minimizes the error ||Ax - b|| (least squares solution) can be found using the pseudoinverse method.

Here's how to use the pseudoinverse method in MATLAB:

main.m
A = [1 2; 3 4; 5 6]; % matrix with more rows than columns
b = [7; 8; 9]; % vector of right-hand sides

% compute the pseudoinverse of A
A_pseudo = pinv(A);

% calculate the least squares solution
x = A_pseudo * b;

% display the solution
disp(x);
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This will output the solution vector x that minimizes the error ||Ax - b||.