ABSTRACT
Linear equations occur in all kinds of mathematical problems. The Toolkit provides two sets of procedures. The routine ELIM carries out Gaussian elimination with the refinement known as pivoting. ELIM should generally be satisfactory in simple cases, but it will not warn the people if the matrix is nearly singular, i.e. if the equations are close to not having a solution, something which can happen frequently. The option read allows a matrix previously saved on a file to be read back, and the order will also be reset. Option matrix displays the matrix and allows its values to be edited. The method described in the chapter is Singular Value Decomposition. The condition number has nothing to do with goodness of fit; with two coefficients (linear regression) the condition number is low, but the regression line fits the data poorly compared to the cases with three and four coefficients.
