Texas Instruments Voyage 200 Manuel

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

3Equations, 3 Unknowns Overdetermined Matrix

Undefined Variable Underdetermined Matrix

More Information

Customer Support Error Messages

TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 2

Important Information

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TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 3

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 4

Entering Data

Entering data manually

1. Start Simultaneous Equation Solver and select New.

2. Enter the number of equations and press D.Values entered

in this dialog box must be integers from 2 to 30.

3. Enter the number of unknowns.

4. Press ¸ ¸ to accept the problem size and display

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 5

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 ƒ1:Load Augmented A|b.

•Press „1:Augmented A|b,2:Coefficient A,3:Constant b,or

4:Two Matrices A and b.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 6

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 ƒ8:Clear All.

Starting a new problem

Press ƒ3:New Problem.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 7

Solving

1. Enter values for the coefficient matrix and values for the right

side. You can enter b1...b5and then select a different

right side.

2. Press ‡to solve the problem. The busy indicator on the

status line displays while the solution is calculated. The

solution values x1. . . xnare displayed in the specified

Exact/Approx mode. The RREF of the augmented matrix can

be shown instead.

If Angle Format is Degree and Complex Format is Polar,

computations are automatically performed numerically.

Displayed as list Displayed as RREF

TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 8

Storing

Once you have entered the coefficients, you can store:

•The augmented matrix (coefficients and the current right

side).

•The coefficient matrix.

•Constant vectors b1...b5.

•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 Show Residuals has been set

to YES in the FORMATS dialog box.

TI-89 / TI-92 Plus / Voyage™ 200 PLT Simultaneous Equation Solver App Page 9

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 b1...b5)you want to

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 10

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 b1iautomatically moves the

cursor to the next ai,1.You can alter the Cursor Movement

direction in the FORMATS dialog box.

•†returns to the Coefficients screen from the Solution

screen.

•A,B,C,or Dmoves 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.

•¤Aor ¤Bon 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 (TI-89) or ˆmenu to insert a column or

row, delete a column or row, or resize the matrix.

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