HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 359

Multiply row 3 by -3, add it to row 1, replacing it: 3\#3#1@RCIJ! Multiply row 2 by -2, add it to row 1, replacing it: 2\#2#1 @RCIJ! Writing this process by hand will result in the following steps: 1 2 3 7 1 2 3 7 1 2 3 7 A aug =  0 1 1 3 0 1 1 3 ≅  0 1 1 1   0 0 − 7 − 14   0 0 1 2   0 0 1 2   1 2 0 1 1 0 0 − 1 Aaug ≅  0 1 0 1 ≅  0 1 0 1 .   0 0 1 2   0 0 1 2   Pivoting If you look carefully at the row operations in the examples shown above, you will notice that many of those operations divide a row by its corresponding element in the main diagonal. This element is called a pivot element, or simply, a pivot. In many situations it is possible that the pivot element become zero, in which case we cannot divide the row by its pivot. Also, to improve the numerical solution of a system of equations using Gaussian or Gauss-Jordan elimination, it is recommended that the pivot be the element with the largest absolute value in a given column. In such cases, we exchange rows before performing row operations. This exchange of rows is called partial pivoting. To follow this recommendation is it often necessary to exchange rows in the augmented matrix while performing a Gaussian or Gauss-Jordan elimination. While performing pivoting in a matrix elimination procedure, you can improve the numerical solution even more by selecting as the pivot the element with the largest absolute value in the column and row of interest. This operation may require exchanging not only rows, but also columns, in some Page 11-33