given matrix a and vertical vector b, find if rank(a)=rank(a|b) in matlab

To find if rank(a) = rank(a|b), where a is a matrix and b is a vertical vector, in MATLAB, you can use the rank function and matrix concatenation ([a,b]) to create the augmented matrix a|b.

Here's an example code snippet that demonstrates how to do it:

main.m
% Given matrix a and vertical vector b
a = [1 2 3; 4 5 6; 7 8 9];
b = [10; 11; 12];

% Compute the ranks of a and [a, b]
rank_a = rank(a);
rank_ab = rank([a, b]);

% Compare the ranks
if rank_a == rank_ab
    disp("rank(a) = rank(a|b)");
else
    disp("rank(a) != rank(a|b)");
end
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Make sure you have the MATLAB Symbolic Math Toolbox installed to use the rank function.