>>10495212The act of performing elimination doesn't have a geometric meaning. It is the same as using substitution to solve for unknowns.
The result that you get from elimination can be interpreted in two ways: it is the point of intersection of a system of planes (a point in n dimensional space that is located on each of the planes in the group) and it is also a linear combination of the columns of the matrix. The x_1, x_2...x_n values of the vector that solves the system are the scalar multiples by which you are multiplying each column of the matrix to get the right hand side. So when you arr given a coefficient matrix and a constant matrix and you solve the system, you consider the constant matrix as a point in R^n you want to get to and you are asking yourself "what linear combination of the columns of the coefficient matrix can get me to this coordinate?"
