LEARNING HOW TO USE AUTOMATED FUNCTIONS

Gauss Elimination

The purpose of this Maple worksheet is to show how to use the automated function

gausselim. There are three modes of the gausselim function: demonstration, interactive

and nostep modes.

> with(linalg) : with(linsys);

Demonstration Mode

The purpose of this version is to display the steps necessary to perform the Gauss elimination

on a given matrix. The user only needs to press the enter key to proceed. Let us look at the

following example. Press Enter at the Maple prompt > to proceed.

> A := matrix ([[1,2,3,4],[9,3,4,1],[2,1,4,5]]);

> gausselim(A);

   1. Demonstration mode

   2. Interactive mode

   3. No Intermediate steps. Just give me the answer

<Select from 1; 2; or 3; >

1;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

Or you may call the function without its argument. As soon as you call the function the program will ask

you to input the matrix A.

> gausselim();

Please enter a matrix to find its row echelon form

A := matrix ([[1,2,3],[0,1,3],[3,1,3]]);

   1. Demonstration mode

   2. Interactive mode

   3. No Intermediate steps. Just give me the answer

<Select from 1; 2; or 3; >

1;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

< type ; and press Enter to continue ?topic for help  exit; to quit >

;

Try your own examples by entering a new matrix A.

Interactive Mode

The purpose of this version is to check whether the user knows how to perform Gauss

elimination on a given matrix. The user must select all row operations (based on a menu)

to perform the Gauss Elimination.Given below is an example in which we have already

entered the inputs that the user is expected to enter while working with this interactive

version of the Gauss Elimination. You may press enter to continue OR select your

own row operations at each level. At any level you may exit the program by typing at

the Maple prompt sign > exit;

> A:=matrix([[28,4,16],[9,1,5],[1,1,1]]);

> gausselim(A);

   1. Demonstration mode

   2. Interactive mode

   3. No Intermediate steps. Just give me the answer

<Select from 1; 2; or 3; >

2;

              OPERATION SELECTION MENU

 1. Multiply row i by c and add it to row j type: 

Rj=Ri*c+Rj  or Rj=c*Ri+Rj;

 2. Interchange row i and row j type : 

Ri<>Rj ; or Ri=Rj

 3. Multiply a row i by constant c type: 

Ri=c*Ri or Ri=Ri*c;

 4. To correct a wrong selction type: 

undo;

 5. To end selections type :  exit;

 6. To see the row echelon form of the matrix type : rowec;

At each step, please enter a row operation in the same format

as in the menu

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R1=R1*(1/28);

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R2=r1*(-8) + R2;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

undo;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R2=r1*(-9) + R2;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R1 = r2;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

r1 = r2;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R3 = (-1)*R1 + R3;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R2 = (-7/2)*R2;

<enter operations as Ri <> Rj or Ri = c*Rj + Ri or Ri = c*Ri >

R3 = (-6/7)*R2 + R3;

You may change the matrix in the above example and select your own operations.

Be sure to delete the previous set of operations first.

Nostep Mode

This mode is equivalent to the Maple gausselim function. Only the final row echelon form

is given. Just press enter to see how it works.

> A := matrix ([[1,2,3,4],[9,3,4,1],[0,1,2,4],[4,5,0,4]]);

> gausselim(A);

   1. Demonstration mode

   2. Interactive mode

   3. No Intermediate steps. Just give me the answer

<Select from 1; 2; or 3; >

3;

Try your own examples by entering a new matrix A.

To return to main menu, move the cursor to next line and press < enter >

> quit;