Hp 48g Graphing Calculator Manual do Utilizador descarregar pdf (Página 182)

100

101

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

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 fMTHI riRTR COL COL+ .

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

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