Computational Algorithm To Find Basis of Linear Equations Solution Set Suppose I have a set of linear equations and I am trying to find out the basis of solution space. For example Check This One. My question is that if there is an algorithm or process which is computationally implementable in a computer program.
You may want
to have a look at Gaussian algorithm or similar pages in the Internet.

It seems that the following is a much better source:
Maxima, search for Function: linsolve ([expr_1, …, expr_m], [x_1, …, x_n])
You may want
to have a look at Gaussian algorithm or similar pages in the Internet.

It seems that the following is a much better source:
Maxima, search for Function: linsolve ([expr_1, …, expr_m], [x_1, …, x_n])