ABSTRACT
The theory developed in Chapter 4 is very elegant. Unfortunately, it presents almost no algorithms to compute actual answers to the questions raised. (The only algorithm in that chapter is Gram-Schmidt orthogonalization.)
This chapter presents two algorithms. The first is Gaussian elimination, which reduces a matrix to row-echelon form, and allows us to solve a system of linear equations, to compute the rank of a matrix, and to compute the coordinates of a given vector relative to a given basis. The second is the computation of the inverse of a matrix.
