1. Press z to display the mode screen. Press †
† ~ Í to select Degreemode. Press † ~
Í to select Par (parametric) graphing mode. Press † † † † ~ ~ Í to select G-T (graph- table) split-screen mode.
2. Press † † † † ~ Í to display the format screen. Press † † † † † ~ Í to select ExprOff.
3. Press o to display the Y= editor for Par graphing mode. Press ™ „ ¤ Í to store cos(T) to X1T. Press ÷ ˜ „ ¤ Í to store sin(T) to Y1T.
4. Press p to display the window editor. Enter these values for the window variables.
Tmin=0 Xmin=L2.3 Ymin=L2.5
Tmax=360 Xmax=2.3 Ymax=2.5
Tstep=15 Xscl=1 Yscl=1
5. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of X1T (cos(T)) is 1 and Y1T (sin(T)) is 0. Press ~ to move the cursor to the next 15¡ angle increment. As you trace around the circle in steps of 15¡, an approximation of the standard value for each angle is highlighted in the table.
Using Split Screen
Setting a Split-Screen ModeTo set a split-screen mode, press z, and then move the cursor to Horiz or G-T and press Í. • Select Horiz (horizontal) to display the graph screen and another screen split horizontally. • Select G-T (graph-table) to display the graph screen and table screen split vertically.
The split screen is activated when you press any key that applies to either half of the split screen.
If stat plots are turned on, the plots are shown along with the x-y plots in graphs. Press y 0 to make the table portion of the split screen active and to display the list data. Press † or } to highlight a value you want to edit, and then enter a new value directly in the table to overwrite the previous value. Press ~ repeatedly to display each column of data (both table and list data). 7. Press y 0 to make the table portion of the
split screen active.
Split-screen display with both x-y plots and stat plots
Some screens are never displayed as split screens. For example, if you press z in Horiz or G-T mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.
When you press a key or key combination in either Horiz or G-T mode, the cursor is placed in the half of the display to which that key applies. For example, if you press r, the cursor is placed in the half where the graph is displayed. If you press y 0, the cursor is placed in the half where the table is displayed.
The TI-84 Plus will remain in split-screen mode until you change back to Full screen mode.
Horiz (Horizontal) Split Screen
Horiz ModeIn Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves.
The top half displays the graph.
The bottom half displays any of these screens.
• Home screen (four lines) • Y= editor (four lines) • Stat list editor (two rows) • Window editor (three settings) • Table editor (two rows)
Moving from Half to Half in Horiz Mode To use the top half of the split screen:
• Press s or r.
• Select a ZOOM or CALC operation.
To use the bottom half of the split screen:
• Press any key or key combination that displays the home screen. • Press o (Y= editor).
• Press … Í (stat list editor). • Press p (window editor). • Press y 0 (table editor). Full Screens in Horiz Mode
All other screens are displayed as full screens in Horiz split-screen mode.
To return to the Horiz split screen from a full screen when in Horiz mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor.
G-T (Graph-Table) Split Screen
G-T ModeIn G-T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves.
The left half displays all active graphs and plots.
The right half displays either table data corresponding to the graph at the left or list data corresponding to the plot at the left.
Moving from Half to Half in G-T Mode To use the left half of the split screen:
• Press s or r.
• Select a ZOOM or CALC operation.
To use the right half of the split screen, press y 0. If the values on the right are list data, these values can be edited similarly to using the Stat List Editor.
Using TRACE in G-T Mode
As you press | or ~ to move the trace cursor along a graph in the split screen’s left half in G-T mode, the table on the right half automatically scrolls to match the current cursor values. If more than one graph or plot is active, you can press } or † to select a different graph or plot.
Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph.
Full Screens in G-T Mode
All screens other than the graph and the table are displayed as full screens in G-T split-screen mode.
To return to the G-T split screen from a full screen when in G-T mode, press any key or key combination that displays the graph or the table.
TI-84 Plus Pixels in Horiz and G-T Modes
TI-84 Plus Pixels in Horiz and G-T ModesNote: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions For Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(:
• In Horiz mode, row must be {30; column must be {94. • In G-T mode, row must be {50; column must be {46.
DRAW Menu Text( Instruction For the Text( instruction:
• In Horiz mode, row must be {25; column must be {94. • In G-T mode, row must be {45; column must be {46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction For the Output( instruction:
• In Horiz mode, row must be {4; column must be {16. • In G-T mode, row must be {8; column must be {16.
Output(row,column,"text")
Note: The Output( instruction can only be used within a program.
Setting a Split-Screen Mode from the Home Screen or a Program To set Horiz or G-T from a program, follow these steps.
1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G-T.
The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.
Note: You also can paste Horiz or G-T to the home screen or program editor from the CATALOG (Chapter 15).
Chapter 10:
Matrices
Getting Started: Using the MTRX Shortcut Menu
Getting Started is a fast-paced introduction. Read the chapter for details.You can use the MTRX shortcut menu (t `) to enter a quick matrix calculation on the home screen or in the Y= editor.
Note: To input a fraction in a matrix, delete the pre-populated zero first.
Example: Add the following matrices: and store the result to matrix C.
1. Press t ` to display the quick matrix editor. The default size of the matrix is two rows by two columns.
2. Press † †to highlight OK and then press Í.
3. Press 2 ~ k 3 ~5 ~ 8 ~ to create the first matrix.
4. Press à t ` † † Í 4 ~ 3 ~ 2 ~ 1 ~ Í to create the second matrix and perform the calculation.
Getting Started: Systems of Linear Equations
Getting Started is a fast-paced introduction. Read the chapter for details.Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form.
6. Press Í to store the matrix to [C].
In the matrix editor (y Q), you can see that matrix [C] has dimension 2x2.
You can press ~ ~ to display the EDIT screen and then select [C] to edit it.
1. Press y . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]. 2. Press 2 Í 4 Í to define a 2×4 matrix. The
rectangular cursor indicates the current element. Ellipses (...) indicate additional columns beyond the screen.
3. Press 1Í to enter the first element. The rectangular cursor moves to the second column of the first row.
Defining a Matrix
What Is a Matrix?A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. You can also define a matrix using the MTRX shortcut menu (t`).The TI-84 Plus has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-84 Plus matrices. Fractions are stored as real numbers and can be used in matrices.
Selecting a Matrix
Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.
1. Press y | to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed.
2. Select the matrix you want to define. The MATRX EDIT screen is displayed. 4. Press 2 Í 3 Í 3 Í to complete the first
row for X + 2Y + 3Z = 3.
5. Press 2 Í 3 Í 4 Í 3 Í to enter the second row for 2X + 3Y + 4Z = 3.
6. Press y 5 to return to the home screen. If necessary, press ‘ to clear the home screen. Press y ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen.
7. Press y 1 to select 1: [A] from the
MATRX NAMES menu. Press ¤ Í. The
reduced row-echelon form of the matrix is displayed and stored in Ans.
1XN1Z =L3 therefore X =L3 + Z 1Y + 2Z = 3 therefore Y = 3N2Z
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are 1 × 1. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension.
• To accept the row dimension, press Í.
• To change the row dimension, enter the number of rows (up to 99), and then press Í. The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press Í, the rectangular cursor moves to the first matrix element.
Viewing and Editing Matrix Elements
Displaying Matrix ElementsAfter you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.
Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.
This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows.
Deleting a Matrix
To delete matrices from memory, use the MEMORY MANAGEMENT/DELETEsecondary menu (Chapter 18).
Viewing a Matrix
The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element
Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.
Using Viewing-Context Keys
Editing a Matrix Element
In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.
1. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions. 2. Press |, }, ~, and † to move the cursor to the matrix element you want to change. 3. Switch to editing context by pressing Í, ‘, or an entry key.
4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context.
Note: You can press ‘ Í to restore the value at the cursor if you make a mistake.
5. Press Í, }, or † to move to another element.
Key Function
| or ~ Moves the cursor within the current row
† or } Moves the cursor within the current column; on the top row, }
moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension
Í Switches to editing context; activates the edit cursor on the bottom line
‘ Switches to editing context; clears the value on the bottom line Any entry character Switches to editing context; clears the value on the bottom line;
copies the character to the bottom line
y 6 Nothing
Using Editing-Context Keys
Using Matrices with Expressions
To use a matrix in an expression, you can do any of the following.
• Copy the name from the MATRX NAMES menu.
• Recall the contents of the matrix into the expression with y K (Chapter 1). • Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.
To enter a matrix in an expression, follow these steps.
1. Press y [[] to indicate the beginning of the matrix. 2. Press y [[] to indicate the beginning of a row.
3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.
4. Press y []] to indicate the end of a row. 5. Repeat steps 2 through 4 to enter all of the rows. 6. Press y []] to indicate the end of the matrix.
The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]]
Any expressions are evaluated when the entry is executed.
Key Function
| or ~ Moves the edit cursor within the value
† or } Stores the value displayed on the edit line to the matrix element;
switches to viewing context and moves the cursor within the column
Í Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor to the next row element
‘ Clears the value on the bottom line
Any entry character Copies the character to the location of the edit cursor on the bottom line
y 6 Activates the insert cursor
Note:
• The commas that you must enter to separate elements are not displayed on output. • Closing brackets are required when you enter a matrix directly on the home screen or in
an expression.
• When you define a matrix using the matrix editor, it is automatically stored. However, when you enter a matrix directly on the home screen or in an expression, it is not automatically stored, but you can store it.
In MathPrint™ mode, you could also use the MTRX shortcut menu to enter this kind of matrix:
1. Press t ` † ~ ~ Í † Í to define the matrix dimension. 2. Press 1 ~ 2 ~ 2 ~ 4 ~ 5 ~ 6 ~ to define the matrix.
3. Press Í to perform the calculation.
Displaying and Copying Matrices
Displaying a MatrixTo display the contents of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press Í.
In MathPrint™ mode:
• An arrow at the left or right indicates additional columns. • An arrow at the top or bottom indicates additional rows.
In Classic mode:
• # or $ in the right column indicate additional rows.
In either mode, press ~, |, †, and } to scroll the matrix. You can scroll the matrix after you press Í to calculate the matrix. If you cannot scroll the matrix, press } ÍÍ to repeat the calculation.
Note:
• You cannot copy a matrix output from the history.
• Matrix calculations are not saved when you change from MathPrint™ mode to Classic mode or vice-versa.
Copying One Matrix to Another To copy a matrix, follow these steps.
1. Press y > to display the MATRX NAMES menu. 2. Select the name of the matrix you want to copy. 3. Press ¿.
4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix.
5. Press Í to copy the matrix to the new matrix name.
Accessing a Matrix Element
On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES menu.
[matrix](row,column)
Using Math Functions with Matrices
Using Math Functions with MatricesYou can use many of the math functions on the TI-84 Plus keypad, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.
Addition, Subtraction, Multiplication
To add or subtract matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.
matrixA+matrixB matrixANmatrixB
To multiply two matrices together, the column dimension of matrixA must match the row dimension of matrixB.
matrixA…matrixB
Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value.
matrix…value value…matrix
Negation
Negating a matrix returns a matrix in which the sign of every element is changed.
Lmatrix
abs(
abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix.
abs(matrix)
round(
round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals (9). If #decimals is omitted, the elements are rounded to 10 digits.
round(matrix[,#decimals])
Inverse
Use the L1 function (œ) or ›L1 to invert a matrix. matrix must be square. The determinant cannot