HP 48g Graphing Calculator - Manual (Page 182)

Gaussian Elimination and Elementary Row
Operations
The systematic process, known as Gaussian elimination is one of the
most common approaches to solving systems of linear equations and
to inverting matrices. It uses the augmented matrix of the system
of equations, which is formed by including the vector (or vectors) of
constants ([&i . . . 6m]) as the right-most column (or columns) of the
14
ts {[aji . . . ^mn])-
■ ail »12 »13 ain bi 1
»21 »22 »23 3'2n
»31 »32 »33 asn b¡
- »ml »1112 »m3 ^mn bm-
To create an augmented matrix:
1. Enter the matrix to be augmented (the matrix of coefficients in the
context of Gaussian-elimination).
2. Enter the array to be inserted (the array of constants in the context
of Gaussian-elimination). It must have the same number of rows as
the matrix.
3. Enter the last column number, n, of the matrix to be augmented in
order to indicate where to insert the array.
4. Press fMTH I r i R T R C O L C O L + .
Once you have an augmented matrix representing a system of linear
equations, then you can proceed with the Gaussian-elimination
process. The process seeks to systematically eliminate variables
from equations (by reducing their coefficients to zero) so that the
augmented matrix is transformed into an equivalent matrix, from
which the solution can be easily computed.
Each coefficient-elimination step depends on three elementary row
operations for matrices;
■ Interchanging two rows.
■ Multiplying one row by a nonzero constant.
B Addition of a constant multiple of one row to another row.
14-18 Matrices and Linear Algebra