Texas Instruments Voyage 200 Manual
2/7/02 ©2001, 2002 Texas Instruments
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
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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