CHAPTER 6

Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200
Note 6A Entering and Editing Matrices
You can enter a matrix into the Data/Matrix Editor or into the Home screen.
Entering a Matrix into the Data/Matrix Editor
a. b. c. d. Press APPS , open the Data/Matrix Editor, and select 3:New. For Type, select Matrix. For Folder, select the folder in which you want to save the matrix. For Variable, type the matrix name. Some names are reserved; if you try to use a reserved name you will get an ERROR message. e. Enter the row and column dimensions of the matrix. f. Press ENTER ENTER to display the matrix on the Data/Matrix Editor screen. Initially all entries are zeros. g. Enter a value into each cell. Press ENTER to register each entry and move the cursor to the next position. You can use fractions and operations when you enter values. h. When you finish entering values, press HOME to return to the Home screen.
Entering a Matrix into the Home Screen
To enter a matrix into the Home screen, use one set of brackets, [ and ], around the entire matrix and one set of brackets around each row. Use commas to separate the entries in a row. Then press STO , type a name for the matrix, and press ENTER. For example, to define the matrix [mat1]
[[23,2,4] [1,3,2]] STO mat1 ENTER.

4 enter 2

Some names are reserved; if you try to use a reserved name you will get an message. Notice that the folder in which the matrix is now stored is indicated in the left corner of the status line. In this example, mat1 is stored in the MAIN folder.

ERROR (continued)

Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200
2004 Key Curriculum Press
Note 6A Entering and Editing Matrices (continued)
TI-89/TI-92 Plus/Voyage 200

Editing a Matrix

To edit a matrix, use the Data/Matrix Editor. a. Press APPS , open the Data/Matrix Editor, and select 2:Open. b. For Type, select Matrix. c. For Folder, select the folder in which the matrix is stored. d. For Variable, select the matrix you want to open and edit. e. Press ENTER to display the matrix on the Data/Matrix Editor screen. f. Arrow to the cell you want to edit. Enter the new value and press ENTER. You can also change the dimensions of a matrix while you are editing by entering a value into a new row or column. Notice that when you create a new row or column the other values in the row or column automatically become zeros. You can then change the zeros to other values. g. When you finish editing, press HOME to return to the Home screen.
Viewing a Matrix on the Home Screen
You can see a complete list of all the matrices stored in your calculator by pressing 2nd [VAR-LINK] and scrolling through the contents of each folder. To see a list of matrices only, press 2nd [VAR-LINK] F2 , for Var Type select Matrix, and press ENTER. To view a matrix on the Home screen, type its name into the entry line and press ENTER. You can also select the matrixs name from the Var-Link screen.

Note 6B Matrix Operations
You can perform operations with matrices just as with numbers. The following examples use matrices [A], [B], and [C].
You can add or subtract matrices if they have the same dimensions.

(continued)

Note 6B Matrix Operations (continued) You can multiply two matrices if the number of columns in the first matrix matches the number of rows in the second matrix. Remember to use the multiplication symbol.
You can multiply any matrix by a constant.
You can raise a square matrix to a power.
The result of a matrix operation can be stored into a matrix or used in the next calculation. You can work recursively with matrices the same way you do with numbers or lists.

Errors

You will get an ERROR:Dimension message if the dimensions of the matrices do not satisfy the operations criteria. If you use a variable that is not defined as a matrix, you may get an error message or an unusual result.
Note 6C Plotting a Polygon
You cannot plot a polygon directly from a matrix, but you can convert a matrix into a list. Then, by dividing the list into two lists, you can plot a polygon. 1 For example, the matrix represents the 2 quadrilateral with vertices (1, 2), (2, 1), (3, 1), and (2, 2). (To graph
Note 6C Plotting a Polygon (continued) a closed figure, the first point must be repeated as the last point.) You can plot the polygon by following these steps: a. Enter the matrix and store it as mat1.
b. On the Home screen, enter 2nd [MATH] 3:List F:mat list(, then type mat1) and press ENTER. c. Arrow up to highlight the list in the bottom line of the history section of the Home screen. Press ENTER.
d. Divide the list, which is now in the entry line, into two lists of equal length by inserting braces, } and {. Store the first list as list l1 and store the second list as list l2. Separate the two storing commands with a colon, 2nd [:].
e. Go to the Y Editor screen, scroll up to Plot 1, and press f. For Plot Type select xyline, for x enter l1, and for y enter l2.

F3 (Edit).

g. Set an appropriate window and display the graph.
[7.9, 7.9, 1, 3.8, 3.8, 1]
Note 6C Plotting a Polygon (continued) You can also use matrices to transform polygons.
Note 6D Matrix Row Operations

The calculator can perform four operations on the rows of a matrix. To exchange two rows in one matrix, use 2nd [MATH] 4:Matrix J:Row ops For example, you exchange rows 1 and 2 of matrix md with the command rowSwap(md,1,2).

1:rowSwap(.

To add the entries of one row to those of another row, use 2nd [MATH] For example, you add the entries of row 1 to those of row 2 and store them into row 2 with the command rowAdd(md,1,2).
4:Matrix J:Row ops 2:rowAdd(.

J:Row ops 3:mRow(.

To multiply the entries of one row by a value, use 2nd [MATH] 4:Matrix For example, you multiply the entries of row 1 by 5 and store them into row 1 with the command mRow(5,md,1).
To multiply the entries of one row by a value and add the products to another row, use 2nd [MATH] 4:Matrix J:Row ops 4:mRowAdd(. For example, you multiply the elements of row 1 by 5, add the products to row 2, and store them into row 2 with the command mRowAdd(5,md,1,2). These commands dont change matrix md; they create a new matrix. Youll probably want to end each command by storing the new matrix with a new name or by replacing md with the new matrix, as was done in each of the examples.
Note 6E Reduced Row-Echelon Form
To convert an augmented matrix to reduced row-echelon form, enter 2nd [MATH] 4:Matrix 4:rref( and the matrix.
This example shows solving the system
x y 2x 7 x 2y 3z 4 2x 2y z 6
to get x 2, y 3, and z 4.

Note 6F Inverse Matrices

To find the inverse of a matrix, raise it to the power of 1.
If you get an ERROR:Dimension message, the matrix is not square; if you get an ERROR:Singular matrix message, one row of the matrix is a multiple of another row. In either case, the matrix has no inverse.
Note 6G Graphing Inequalities
Graphing an inequality is like graphing an equation except you select a graph style to shade above or below the boundary line. The calculator always graphs a solid line for the boundary regardless of the type of inequality. a. Enter the boundary line equation into the Y Editor screen and press ENTER. b. Highlight the boundary line equation, then press 2nd [F6] (Style). (On a TI-92 Plus or a Voyage 200, press F6.) c. Select 7:Above to shade above the boundary line, or select 8:Below to shade below the boundary line. d. Set an appropriate window and then display the graph.
Note 6G Graphing Inequalities (continued) Vertical boundary lines can be approximated with a line of very steep negative slope. An equation in the form y 1000(b x), where b is the x-intercept, works well. These screens show an approximation for x 3.

[2, 8, 1, 1, 6, 1]

Graphing Systems of Inequalities
When graphing a system of inequalities, it is often easier to do reverse shading so that the feasible region is the area not shaded. To do this, shade above the boundary line for the inequalities and , and shade below the boundary line for the inequalities and. Vertical boundary lines can be approximated with a line of very steep negative slope. These screens show the region defined by the intersection of

y6x y5 x4 y0 x0

CHAPTER 2
Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

Note 2A Naming Lists

See Note 1G: Naming and Storing Data.

Note 2B Analyzing Data

You can get several standard statistics for a stored data set.
Analyzing Data Stored as a Data Variable
a. Press APPS and open the Data/Matrix Editor. b. Open the data variable that contains the data you want to analyze. (See Note 1G if you need help displaying a data variable.) c. Press F5 (Calc). d. For Calculation Type select 1:OneVar. Arrow down to make the next selection. Do not press ENTER. e. For x enter the column name that contains the data you want to analyze. f. If the frequencies of the data values are stored in another column, change Freq and Categories? to YES, and then for Freq enter the column name that contains the frequencies. g. Press ENTER ENTER.
Analyzing Data Stored as a List Variable
If you open data stored as a list variable in the Data/Matrix Editor, you cannot follow the procedure used for data variables because the F5 (Calc) menu is not active. a. Press APPS and open the Stats/List Editor. (See Note 1G for help opening the Stats/List Editor.) Make sure to open the folder that contains your list variable. You can press 2nd [VAR-LINK] and scroll down to see a display of the list variables in each folder. Alternatively, if the calculator does not have the Stats/List Editor application, you can open the Data/Matrix Editor and open any data variable from the folder containing the list variable you want to analyze. (See Note 1G if you need help displaying a data variable.) b. Press F4 (Calc) if you are in the Stats/List Editor (press F5 (Calc) if you are in the Data/Matrix Editor). c. Select 1:1-Var Stats when using the Stats/List Editor (select 1:OneVar if you are in the Data/Matrix Editor). d. In the Stats/List Editor, for List enter the name of the list variable that you want to analyze. If your data is in one of the set lists enter list1 or list2 etc. (In the Data/Matrix Editor enter your list name for x.)

(continued)

Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200
2004 Key Curriculum Press
Note 2B Analyzing Data (continued)
TI-89/TI-92 Plus/Voyage 200
e. If the frequencies of the data values are stored in another list, for Freq enter the name of the list variable that contains the frequencies. (In the Data/Matrix Editor, change Freq and Categories? to YES in order to make Freq active.) f. Press ENTER ENTER. For either a data variable or a list variable, these values will be displayed.
x x x 2 Sx x nStat minX q1 MedStat q3 maxX (x x )2
the mean. the sum of the x-values. the sum of the squares of the x-values. the sample standard deviation. the population standard deviation (available only in the Stats/List Editor). or n the number of items in the list. the minimum data value. or Q1X the first quartile. or MedX the median. or Q3X the third quartile. the maximum data value. the sum of the squares of the deviations (available only in the Stats/List Editor).
You can display some of these statistics individually for a list variable, such as the mean and median. Press 2nd [MATH] 6:Statistics.

Note 2C Box Plots

The calculator can display up to nine box plots at once. First set up each plot, and then set up the window. For help setting the Plot Setup screen see Note 1H. There are two types of box plots.

3:Box Plot

is the usual box plot that shows all data in one of the four quartiles.
marks outliers as special. The calculator uses the standard rule for defining an outlier: Values greater than Q3 1.5 IQR or less than Q1 1.5 IQR are outliers. If you select this modified box plot, you must choose what mark to use for an outlier.
5:Mod Box Plot (continued)
Note 2C Box Plots (continued) For either box plot, set x to be the name of the list variable (or the column of the current data variable) that you want to plot. Press ENTER ENTER. Next go to the Window Editor screen. See Note 1H for help determining the window values to use. In a box plot, ymin, ymax, and yscl can be any value as long as ymin is less than ymax. Then press [GRAPH]. below is a box plot using the data in column c1. Plot2 and Plot3 use the data in column c2. Data in Plot3 have frequencies set out in column c3. Plot3 is also a modified box plot showing outliers.
In the Graph screen shown here, the axes are turned off. To turn axes off (or on) press F1 9:Format on the Graph screen. On the GRAPH FORMATS screen, arrow down to Axes and select the option you want.

Note 2D Histograms

To plot a histogram, set the Plot Setup screen as directed in Note 1H. Choose a Hist. Bucket Width (or bin width) so there are not too many or too few bins in your graph. A good rule is to set the bucket width at about 15% of the range. Bucket width will be the xscl value on your Window Editor screen.

Now set your Window Editor screen. Setting a good window to view a histogram may take several tries.

xmin xmax xscl ymin

a multiple of bucket width that is less than or equal to your smallest value. a multiple of bucket width that is greater than your largest value. bucket width. a negative value to keep the labels from covering the bins when you trace. The size of the negative number you need depends on the height of the bins set by ymax. Start with 1. the number of items in your tallest bin. This will probably be a guess; start with half the number of items in your data set. the distance between tick marks on the y-axis. The number you choose will depend on the range of y-values. If the tick marks are too close together the y-axis will appear too thick. This number does not affect a histogram.

ymax yscl

xres 1.
Note 2D Histograms (continued) Press [GRAPH]. If the plot doesnt fit well in the window, press F3 (Trace) and arrow left or right to find the number of items in the tallest bin. (This is n: at the bottom of the screen.) Go back to the Window Editor screen and reset ymax (and ymin if needed) and then display the plot again. These screens show the setup for two plots. Plot1 shows a histogram using the data set {22, 25, 25, 27, 27, 27, 28, 28, 29, 31, 32, 32, 37} listed in column c1. Plot2 shows a histogram of the same data but the values are given in column c2, and their corresponding frequencies (number of occurrences) are given in column c3. Frequencies are usually used only for very large data sets.
In either case, the range is 15. Fifteen percent of that is (15)(0.15) 2.25, so bucket width is set at 2. There are 13 data points, so ymax 6.5. The histogram in the second screen is too short, so the window is adjusted.