Notes
1. Depending on the speed of your computer, it may take a while for the applet to get going. If nothing appears, it could mean that your browser is not Java-capable, so we suggest you go to Netscape's Home and download Netscape 3.xx. Alternatively, try adjusting the window size to force it to appear.
2. This is a slightly revised version of the original posted pivot program (Version 1.1). The major change is that, in version 1.1 you had to press a "accept changes" button to get the program to recognize your manual editing of the spreadsheet. However, this did have the advantage that switching back and forth between fraction and decimal modes casued no loss in accuracy, so we have left Version 1.1 posted here if you prefer to use it.)

We suggest you use a wide window.

Warning and Disclaimer This is a rough and ready piece of software. Please do not expect it to perform flawlessly at all times. Also don't forget that Java-capable browsers are still in their infancy, and therefore prone to crash unpredictably, so it is imperative to ensure that all your important files are saved before you use the applet. Of course, we would very much like to learn of any bugs, so please email us if you have found one.

The legal stuff: The authors assume no liability for damage or loss to your data or your equipment resulting either directly or indirectly from your use of this applet.

Now, the fun stuff.

You should see a grid of cells, something like a spreadsheet. The frst row consists of labels, while the rows below it are for entering data.

The Labels The first row (seperated a little from the others) contain the names of the columns: x1, x2, x3, and so on. They are there simply to help you keep track of the unknowns or variable names. You can change them to anything you like, such as x, y, z, s, t, u. (Pressing "Erase Matrix" button changes them back to their default names.)

The area under the heading row is for data entry.

Entering Data You can type in the matrix entries just as you would in a spreadsheet. However, depending on the platform and browser, you may have to use the mouse to go from cell to cell; in some platforms and browsers the tab key works. The format you should use depends on the Mode setting -- see below. Areas you leave blank are simply ignored, just as in a spreadsheet . (Actually, they are taken to be zero.) When you have entered all the data, we suggest you press the "Save This" button so that you can revert back to this matrix later.

Modes This matrix pivot applet operates in two modes: Fraction Mode and Decimal Mode. To change from one mode to the other at any time during the computation, double-click the selection on the top left above the spreadsheet. (Just selecting without double-clicking will probably not be enough.)

• Fraction Mode This is the more accurate mode, and also the default setting of the applet. In Fraction Mode, you must enter all numbers as either (positive or negative) whole numbers or fractions of up to six digit numbers.

   Examples:   123       -123456       11/33       -22/100      
  		6/1       0       445566/112233

  
  No spaces, decimals, commas, tabs or any other characters, please. Thus, for example, 0.45 should be entered as 45/100.

• Decimal Mode This is the mode in which all data is entered in decimal form. In Decimal Mode, all numbers should be entered as either (positive or negative) whole numbers or decimals using 6 or fewer significant digits to the right of the decimal.

   Examples:   1.23456       -133.2       0.334455       123       0
  		0.000123456   but not -12345600

  
  No spaces, slashes, commas, tabs or any other characters, please. Thus, for example, 2,346 should be entered as 2346.

  It is strongly suggested that you work in fraction mode. This will allow you to enter the data more accurately. (All the actual calculations are done using fractions.) Switching back and forth between Fraction and Decimal Modes will result in loss of accuracy due to rounding of decimal approximations to fractions.

  Switching Modes -- An Example Entering 1/3 in Fraction Mode and then converting to Decimal Mode changes the entry (on the table) to 0.333333. Switching it back to Fraction Mode will give you the fraction 333333/1000000, which is close to, but not equal to 1/3.

Revert, Accept Changes, Erase Matrix The "Revert" button can be pressed at any time to go back to the matrix that was visible when you last pressed "Save This." As for the "Erase Matrix" button, it does what you expect...

Reducing the Matrix To reduce a matrix, simply follow the instructions in the tutorial:

• Make sure you have entered the numbers in the correct format.
• (Optional) Clear all fractions by multiplying each row by a common denominator. To multiply a row by a number, just fill in the appropriate boxes and press "Do It." For example, to multiply Row 3 by 6, see the figure.

• (Optional) In the same way, you can also divide any row by any number (to "simplify" the row -- see the tutorial).
• Select the leading entry (first non-zero entry) in row 1 (by highlighting it in the usual way) and then pivot on the selected entry by simply pressing "Pivot on Selection."
• Repeat the above step for the subsequent rows.
• Turn each of the leading entries into 1's by in turn selecting them and pressing "Divide Row By Selection."
• Rearrange the rows, if necessary, by using the "Swap Rows" option (and pressing "Do It.")

Pivoting Without Fractions If there are no fractions or decimals in your matrix (possibly after you have cleared the fractions using the first step above) and you leave it in Fraction Mode, then pivoting will be automatically done using the method described in the text "Finite Mathematics Applied to the Real World," so that all the entries will remain whole numbers.

If, on the other hand, your matrix contains one or more fractions (or decimals) when you tell it to pivot (or you have it in decimal mode) you can expect fractions (or decimals) to proliferate, since it will pivot using the "standard" method.

Enjoy!