Texas instruments TI-92 PLUS, VOYAGE 200 Simultaneous Equation Solver

TI
TI-89/TI-92 Plus/Voyage™ 200 Simultaneous Equation Solver
How To………
Start the Application Store Values Enter Data Navigate Solve a Problem Change Format
Examples
3 Equations, 3 Unknowns Overdetermined Matrix Undefined Variable Underdetermined Matrix
More Information
Customer Support Error Messages
2/7/02 © 2001, 2002 Texas Instruments

Important Information

Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis.
In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed any applicable purchase price of this item or material. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
Graphing product applications (Apps) are licensed. See the terms of the license agreement
for this product.
Microsoft, Windows, Windows NT, Apple, Macintosh, Mac, and Mac OS are trademarks of their respective owners.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 2

What Is Simultaneous Equation Solver?

Simultaneous Equation Solver finds solutions to systems of linear equations. It provides a convenient, easy-to-use interface to simplify setting up a problem, solving it, and exploring the solution. You can:
Enter, load, and edit coefficient matrices and up to five vectors representing different right sides.
Store the solution as a vector (an nx1 matrix).
Display solutions as a list of values or in reduced row
echelon form (RREF).
Solve over-determined systems of equations (systems in which there are more equations than unknowns).
Solve under-determined systems of equations (systems in which there are fewer equations than unknowns).
Solve systems containing both numeric and symbolic coefficients.
Identify whether a given system has a unique solution, an infinite number of solutions, or no solution.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 3

Entering Data

Entering data manually

1. Start
2. Enter the number of equations and press D. Values entered
3. Enter the number of unknowns.
4. Press ¸ ¸ to accept the problem size and display
Simultaneous Equation Solver and select New.
in this dialog box must be integers from 2 to 30.
the matrix. The first coefficient is selected, and its matrix row and column designators are displayed on the entry line.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 4
5. Enter the first coefficient and press ¸. The cursor returns to the matrix and moves to the next column (right). You can change the cursor to move to the next row (down) instead in the
FORMATS dialog box.
You can enter a real or complex value or an expression that resolves to a real or complex value. You can also enter symbolic data.

Loading existing data

You can load an existing matrix as all or part of the problem from within Simultaneous Equation Solver by using either of the following methods.
Press ƒ
Press
4:Two Matrices A and b.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 5
1:Load Augmented A|b. 1:Augmented A|b, 2:Coeffi cien t A, 3:Constant b, or

Editing coefficients

1. Move the cursor to a coefficient and press ¸. The cursor moves to the entry line.
2. Edit the value and press ¸. The new value appears in the matrix.

Clearing coefficients

Press ƒ
8:Clear All.

Starting a new problem

Press ƒ
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 6
3:New Problem.

Solving

1. Enter values for the coefficient matrix and values for the right side. You can enter b
right side
.
2. Press ‡ to solve the problem. The busy indicator on the status line displays while the solution is calculated. The solution values x
1
Exact/Approx mode. The RREF be shown instead.
. . . b5and then select a different
1
. . . xnare displayed in the specified
of the augmented matrix can
Displayed as list
Displayed as RREF
If Angle Format is Degree and Complex Format is Polar, computations are automatically performed numerically.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 7

Storing

Once you have entered the coefficients, you can store:
The augmented matrix (coefficients and the current right side).
The coefficient matrix.
Constant vectors b
. . . b5.
1
An individual element of a coefficient matrix or constant vectors.
Once you have calculated the solution, you can also store:
The solution as a vector (an nx1 matrix).
An individual element of a solution.
The RREF matrix.
The residual vector, provided
to
YES in the FORMATS dialog box.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 8
Show Residuals has been set
From either the Coefficients screen or Solution screen, press and select
1:Augmented A|b, select a folder, and enter a name. You
can also do this from ƒ.
2:Coefficient A, select a folder, and enter a matrix name.
3:Constant b, select a folder, enter a name and indicate
which right side contents (vectors b
. . . b5) you want to
1
store. The values are stored as a vector (an nx1 matrix).
4:Solution x, select a folder, and enter a name. The
values are stored as a vector (an nx1 matrix).
5:RREF Matrix, select a folder, and enter a name.
6:Residuals, select a folder, and enter a name. The
values are stored as a vector (an nx1 matrix).
To store individual coefficients or roots from the Coefficients or Solution screen:
1. Place the cursor on the value you want to store.
2. Press §.
3. Enter a variable name, and then press ¸.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 9

Navigating Within Simultaneous Equation

¸ moves the cursor to the next coefficient in the equation or to the next equation, unless you change the Cursor Movement direction in the
FORMATS dialog box.
Pressing ¸ after entering b1 cursor to the next a direction in the
FORMATS dialog box.
. You can alter the Cursor Movement
i,1
automatically moves the
i
† returns to the Coefficients screen from the Solution screen.
A, B, C, or D moves among the coefficients for editing.
2 A or 2 B on the entry line moves the cursor to the
beginning or end of the value.
¤ A or ¤ B on the entry line highlights characters for copying.
¥ A, ¥ B, ¥ C, or ¥ D moves the cursor to the beginning or end of the row or column.
2 A, 2 B, 2 C, or 2 D in the matrix moves the cursor one page.
Use the 2 ˆ ( T I-89) or ˆ menu to insert a column or row, delete a column or row, or resize the matrix.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 10
If the Split Screen mode is set to Top-Bottom when the application is started, the TI-89 automatically switches to
Full; the TI-92 Plus / Voyage™ 200 PLT automatically places
the application in the top portion.
To see the solution displayed in RREF, press ‡ from the Solution screen.
If another application is running, 2 a toggles between the applications.

Right sides

To enter additional right sides (b
through b5), use the cursor
2
to move to those cells.
To select a different right side to use in a calculation, use the 2 ‰ (TI-89) or menu.
1:Augmented A
additional right sides separately, use the
b stores only the current b. To store

3:Constant b
command.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 11

FORMATS Dialog Box

To display the FORMATS dialog box, press ƒ 9:Format or shortcut keys ¥ Í (TI-89) or ¥ F.

Format settings

Column Width: Sets the number of characters to display in each
column. The default is 6. (Do not confuse this option with the
MODE setting Display Digits, which determines the number of
digits displayed.)
Cursor Movement: Determines whether the cursor moves to the
next column (right) or next row (down) after data are entered. The default is Right.
Answer in RREF: Sets the default Solution screen display mode
when the system is solved the first time. If displayed in list form. If
YES, the solution is displayed in RREF
NO, the solution is
form. The default is No.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 12
Show Residuals: Toggles display of the residual vector b-Ax,
where x is the computed solution. The default is No. When Show Residuals is set to
the column to the right of b
YES, residuals are displayed in
on the Coefficients screen. |resid| is
5
the magnitude of the difference between the coefficient matrix times the computed solution and the right side. (For example, resid
i=ai,1¦x1+ai,2¦x2
…a
i,n¦xn-bi
, where i=1…n.) The entry line
shows the current residual element.
Tolerance: Default sets the tolerance to
5E-14¦max(dim(Augmented matrix)) ¦rownorm(Augmented matrix).
User-Defined enables the Tolerance field, where you can enter a
preferred tolerance level.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 13

Example — Three Equations, Three Unknowns

1. Press 3 „ and set Exact/Approx to Exact.
2. Start
3. Press
Simultaneous Equation Solver and select New.
3 D 3 ¸ ¸ for a problem with three equations
and three unknowns.
4. Enter the coefficients: a
1,1
a
2,1
a
3,1
= 9 a = 5 a = 1 a
= 8 a
1,2
= M6 a
2,2
= 5 a
3,2
= 7 b11= 2
1,3
= M4 b12= 2
2,3
= 9 b13= 7
3,3
5. Press ‡ to solve the problem. The busy indicator on the status line displays while the solution is calculated.
The values for x
x1= 72à481
= M547à481
x
2
= 670à481
x
3
, x2, and x3are displayed:
1
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 14

Example — Undefined Variable

1. Press 3 „ and set Exact/Approx to Exact.
2. Start
3. Press
Simultaneous Equation Solver and select New.
3 D 3 ¸ ¸ for a problem with three equations
and three unknowns.
4. Enter the coefficients: a
1,1
a
2,1
a
3,1
= 2 a = 3 a = 3 a
= 3 a
1,2
= M1 a
2,2
= 2 a
3,2
= M2 b11= M3
1,3
=unk b12= M2
2,3
= M1 b13= M1
3,3
5. Press ‡ to solve the problem according to the mode setting. The busy indicator on the status line displays while the solution is calculated.
The values for x
, x2, and x3are displayed:
1
x1= 26à(5(5unkN7))+3/5
= M104à(5(5unkN7)) N7à5
x
2
= M26à(5unkN7)
x
3
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 15
6. Press 3 „ and set Exact/Approx to Approximate. The solution is automatically recalculated and expressed as:
x1= 1.04à(unkN1.4)+.6
= M4.16à(unkN1.4) N1.4
x
2
x
= M5.2à(unkN1.4)
3
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 16

Example — Overdetermined Matrix

1. Press 3 „ and set Exact/Approx to Exact.
2. Start
3. Press
Simultaneous Equation Solver and select New.
5 D 3 ¸ ¸ for a problem with five equations
and three unknowns.
4. Enter the coefficients: a
= 9 a
1,1
a
= M9 a
2,1
a
= M9 a
3,1
a
= M4 a
4,1
a
= 1 a
5,1
= M6 a
1,2
= 9 a
2,2
= 4 a
3,2
= M4 a
4,2
= M9 a
5,2
= 2 b11= 6
1,3
= M4 b12= M1
2,3
= M9 b13= M7
3,3
= 9 b14= 7
4,3
= M7 b15= 8
5,3
5. Press ‡ to solve the problem. The busy indicator on the status line displays while the solution is calculated.
The display shows
No solution found.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 17
6. Press ‡ again to view the RREF matrix.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 18

Example — Underdetermined Matrix

1. Press 3 „ and set Exact/Approx to Exact.
2. Start
3. Press
Simultaneous Equation Solver and select New.
3 D 5 ¸ ¸ for a problem with three equations
and five unknowns.
4. Enter the coefficients: a
= 3 a
1,1
a
= M1 a
2,1
a
= M9 a
3,1
= 8 a
1,2
= M7 a
2,2
= M9 a
3,2
= 3 a
1,3
= M2 a
2,3
= M8 a
3,3
= 1 a
1,4
= 7 a
2,4
= 2 a
3,4
= 4 b11= 9
1,5
= 4 b12= 4
2,5
= 2 b13= M2
3,5
5. Press ‡ to solve the problem. The busy indicator on the status line displays while the solution is calculated.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 19
The display shows two arbitrary constants (@1 and @2) and an infinite number of solutions expressed in terms of those constants:
x1= L307@1à32N155@2à16+15 x
= L37@1à32N29@2à16+3
2
= 395@1à32+211@2à16N20
x
3
= @1
x
4
x
= @2
5
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 20

Errors, Error Messages, and Restrictions

Message Description
The variables used in the editor need to be defined as real or non-real numbers.
Coefficient A and Constant b matrices do not have the same number of rows.
Memory
Element value must be a scalar or scalar expression.
Coefficients can contain undefined variables (variables with no ass igne d value), but the variable type is limited to real numbers and non-real numbers.
This occurs only when the matrices specified from 4:Two Matrices A and b are incompatible sizes.
Simultaneous Equation So l ver requir es at least 6000 bytes of RAM to run properly. When the amount of available RAM falls below this threshold, the application may display an
Error: Memory dialog box and
return to the Home screen or simply exit to the Home screen. If this occurs, archive or delete some variables before returning to the application.
Only scalar expressions are accepted as input. When using a variable as input, verify that it is not a list, matrix, or other non-scalar expression. Choose a different variable that is scalar.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 21
Message Description
Existing variable SMLTDATA is preventing TISMLTEQ from saving its place. Press ENTER to write over the existing variable.
TISMLTEQ.simult is incompatible with cylindrical and spherical vector formats and with hex and bin bases.
Tolerance value must be a nonnegative real number.
This error message appears when the SMLTDATA variable is archived or locked. Unlock or unarchive the SMLTDATA variable.
Change the vector format mode to rectangular and the base mode to DEC (decimal).
User-defined tolerance in the FORMATS dialog box must be zero or a positive real number.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 22

Installing Simultaneous Equation Solver

Detailed Flash application installation instructions are available from education.ti.com/guides
You will need:
A TI-89 / TI-92 Plus / Voyage™ 200 PLT with the latest Advanced Mathematics Software Operating System. Download a free copy from
education.ti.com/softwareupdates
A computer using either Microsoftë Windowsë or Appleë Macintoshë operating system software.
A TI-GRAPH LINK™ computer-to-calculator cable, available for purchase from the TI Online Store at
education.ti.com/buy
Either TI Connect™ software or TI-GRAPH LINK connectivity software for the TI-89 / TI-92 Plus. Download a free copy from education.ti.com/softwareupdates
.
.
.
.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 23

Starting and Quitting the Application

Starting Simultaneous Equation Solver

The instructions in this guidebook refer to this Flash application only. For help using this product, refer to the comprehensive guidebook at education.ti.com/guides
.
1. Press Œ and select
Simultaneous Eqn Solver.
2. Select the problem type from the menu.
Current returns to the screen you were on when you left
Simultaneous Equation Solver.
Open lets you select an existing matrix as an augmented
A|b matrix to use.
New creates a new problem.

Quitting Simultaneous Equation Solver

Press 2 K from any screen.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 24

Deleting an Application

Deleting an application removes it from the handheld device and increases space for other applications. Before deleting an application, consider storing it on a computer for reinstallation later.
1. Quit
2. Press 2 ° to display the
the application.
VAR-LINK [ALL] screen.
3. Press 2 ‰ (TI-89) or to display the list of installed applications.
4. Select the application you want to delete.
5. Press ƒ
1:Delete. Th e VAR-LINK delete confirmation dialog
box displays.
6. Press ¸ to delete the application.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 25

Texas Instruments (TI) Support and Service Information

For general information

E-mail: ti-cares@ti.com Phone: 1-800-TI-CARES (1-800-842-2737)
For US, Canada, Mexico, Puerto Rico, and Virgin Islands only
Home page: education.ti.com

For technical questions

Phone: 1-972-917-8324

For product (hardware) service

Customers in the US, Canada, Mexico, Puerto Rico, and Virgin Islands:
returning a product for service.
Always contact TI Customer Support before
All other customers: Refer to the leaflet enclosed with your
product (hardware) or contact your local TI retailer/distributor.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 26

TEXAS INSTRUMENTS LICENSE AGREEMENT

BY INSTALLING THIS SOFTWARE YOU AGREE TO ABIDE BY THE FOLLOWING PROVISIONS.
1. LICENSE: Texas Instruments Incorporated (“TI”) grants you a license to use and copy the software program(s) (“License Materials”) contained on this diskette/CD/web site. You, and any subsequent user, may only use the Licensed Materials on Texas Instruments calculator products.
2. RESTRICTIONS: You may not reverse-ass emble or revers e-comp il e the Licensed Materials. You may not sell, rent, or lease copies that you make.
3. COPYRIGHT: The Licensed Materials and any accompanying documentat i on are copyrighted. If you make copies, do not delete the copyright notice, trademark, or protective notices from the copies.
4. WARRANTY: TI does not warrant that the Licensed Materials or documentat i on will be free from errors or that they will meet your specific requirements. THE LICENSED MATERIALS ARE PROVIDED “AS IS” TO YOU OR ANY SUBSEQUENT USER.
5. LIMITATIONS: TI makes no warranty or condition, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding the Licensed Materials.
IN NO EVENT SHALL TI OR ITS SUPPLIERS BE LIABLE FOR ANY INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, LOSS OF PROFITS, LOSS OF USE OR DATA, OR INTERRUPTION OF BUSINESS, WHETHE R THE ALLEGED D AM A GES ARE LABELED IN TORT, CONTRACT, OR INDEMNITY.
SOME STATES OR JURISDICTIONS DO NOT ALLOW THE EXCLUSION OR LIMITATION OF INCIDENTAL OR CONSEQUENTIAL DAMAGES, SO THE ABOVE LIMITATION MAY NOT APPLY.
IF YOU AGREE TO BE BOUND BY THIS LICENSE, CLICK ON THE “ACCEPT” BUTTON; IF YOU DO NOT AGREE TO BE BOUND BY THIS LICENSE, CLICK ON THE “DECLINE” BUTT ON TO EXIT THE INSTALLATION.
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 27
Page Reference
This PDF document contains electronic bookmarks for on-screen navigation. If you print this document, use the page numbers below to find specific topics.
Important Information............................................................................................2
What Is Simultaneous Equation Solver?.............................................................. 3
Entering Data........................................................................................................ 4
Solving..................................................................................................................7
Storing ..................................................................................................................8
Navigating Within Simultaneous Equation .........................................................10
FORMATS Dialog Box........................................................................................ 12
Example — Three Equations, Three Unknowns ................................................14
Example — Undefined Variable .........................................................................15
Example — Overdetermined Matrix ...................................................................17
Example — Underdetermined Matrix .................................................................19
Errors, Error Messages, and Restrictions........................................................... 21
Installing Simultaneous Equation Solver ............................................................ 23
Starting and Quitting the Application .................................................................. 24
Deleting an Application.......................................................................................25
Texas Instruments (TI) Support and Service Information................................... 26
TEXAS INSTRUMENTS LICENSE AGREEMENT ............................................27
TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 28
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