how to calculate the row space of a matrix in matlab

To compute the row space of a matrix A in MATLAB, we can use the rref function and extract the rows with pivot columns as they form a basis for the row space. The following code demonstrates this:

% Define a matrix A
A = [1 2 3; 4 5 6; 7 8 9];

% Compute the row-reduced echelon form of A
rrefA = rref(A);

% Find the indices of the pivot columns
ind = find(any(rrefA,2));

% Extract the corresponding rows from the original matrix
rowSpaceA = A(ind,:);

% Display the row space
disp("Row space of A:");
disp(rowSpaceA);
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The output should be:

main.m
Row space of A:
   1   2   3
   4   5   6
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This means that every row of A can be written as a linear combination of the rows of rowSpaceA.

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