Hp 39g Graphing Calculator Manual do Utilizador descarregar pdf (Página 188)

Reduced-Row

Echelon Form

The following set of equations x~2y + 3z = 14

2x + y-z = ^3

4x-2y + 2z = 14

can be written as the augmented matrix

which can then stored as a

3x4 real matrix in Ml.

1 -2 3

2 1 -1 -3

4 -2 2 14_

Ml11 2

3 4

1 -s

3 IH

-1 -3

d H

-s s IH

You can use the RREF

function to change this to

reduced row echelon form,

storing it as M2 for

convenience.

The reduced row echelon

matrix gives the solution to

the linear equation in the

forth column.

RREF Oil >W2

[[1,0,8, n,C0,l»0!-23.

1 2 3

1 1 0

0 1

? (1

1 0 -a

0 1 3

An advantage of using the RREF function is that it will also

work with inconsistent matrices resulting from systems of

equations which have no solution or infinite solutions.

For example, the following set of equations has an infinite

number of solutions:

A' + y -z = 5

2.t--v = 7

x^2y + z = 2

The final row of zeros in the

reduced-row echelon fonn of

the augmented matrix

indicates an inconsistency.

ME 1

2 3 4

1 0

-.333334

F 1

-.SÉÉ6? 1

0 0

12-14

Matrices

1 2 ... 183 184 185 186 187 188 189 190 191 192 193 ... 291 292

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