General Tips

             Interactive Tips

 While the program is in use, there is a small window, titled Display Screen, that is first displayed at the lower right hand side of the main window. While the program executes, you can find interactive tips and help in this window. Often, this answers your questions and tells you what to do next.

Shortcuts

The primary menu items have shortcut keys assigned to them. To use the shortcut keys, simply hold down control and then press whatever key is appropriate. To find out what the shortcut key is, consult the menu item that you would like to shortcut – that menu item’s shortcut key is listed next to it.

Getting Started

The Linear Mathematics Applet was designed to offer flexibility of operation and provide a calculation tool for a Linear Mathematics course (in particular, NKU's MAT111 course). You will find that there are certain things that need to be done to perform calculations with the Linear Mathematics applet with every use, and the general procedure of those things is listed below. Somewhat further along, you will find a brief explanation of how to do the primary calculations used in a Linear Mathematics course, as they are presented in the NKU MAT111 Linear Mathematics textbook. The basic functions are described here, however they may be used in any number of combinations, assuming that the operations are legal, such that an almost infinite possible

                First Steps 

1. All calculations in this software are performed on a matrix of some type. There are three options for this in the software. In terms of the software, you need to decide if you want a more general matrix, or the more specific type of matrix, the Tableau. After you decide this, select the appropriate menu and press create. If you chose a matrix, decide if you want an augmented matrix, and then enter rows and columns. For tableau, simply enter rows and columns, but be sure to follow the specialized rules about the dimensions of tableaus.

 2.  After you've created your matrix, a matrix of cells with 0's in them will appear in the main window.   In these, you should enter the values for each cell in your matrix. If the dimensions aren't right, then you need to create a new matrix (or tableau) again and change them. If you make a mistake while entering values, you can just select edit on the menu to correct this problem later. After you are done entering values, press enter on the input frame that is normally found to the right of the main frame.

3. Once everything has been entered, you can start performing whatever calculation you like. Order does not matter, and you are only restricted by those functions that are legal for the matrix you entered. It is possible to emulate one function by manually performing a series of other operations. For example, you can get the effect of using the reduce operation by a series of pivots.

How To

                All of the following assume you have already completed the basic steps listed above to create a matrix/tableau and get it ready for operation. At any point, as long as the matrix is entered, and mathematical conditions are satisfied; the following operations may be performed. To access each operation, simply click that menu item in the appropriate (either Tableau or Matrix) menu.

                 Pivot

                There are two options when performing a pivot. You may either enter the row and column of the pivot element in the input window, or you may click on an element in the matrix. If you choose to do it by clicking with the mouse, the program will give you visual feedback. If you the cell that the mouse cursor is currently over is a valid pivot point, it's background will turn green. Otherwise, the background of the cell will turn red.

                 Edit An Already Created Matrix

                 After selecting the edit item, you will find that the matrix cells appear as they did when you first entered the matrix, but with the current values in them. To edit the matrix, simply change whichever values you like and then press the enter button on the input frame.

                 Take a Power of A Matrix

                 This operation can only be performed on a square matrix. After the matrix is entered, select power and enter the power, then press the take power button. The matrix, taken to the given power, will appear in a new window. After it appears, you may then multiply it on the left or the right by another matrix.

                 Multiply a Matrix by another Matrix

                 Because matrix multiplication is not commutative, you can either multiply the matrix currently entered on the right or on the left. This means that we put the new matrix, the one you wish to multiply the current matrix by, on the left or the right. Depending on which side you multiply on, either the rows or columns of the new multiplicand is predetermined. This is taken care of for you by the program. Simply enter the other dimension, and press create. Then, enter the values of the multiplicand and press multiply when finished. The result will appear in the same window as the original, with the multiplicand window being destroyed.

                 Find the Inverse of a Matrix Automatically

                 This operation may only be performed on a square matrix. After entering, select find inverse automatically and the inverse will appear in a new window. If an inverse is not possible, a new window will convey that message.

                 Find the Inverse of a Matrix Manually

                 This operation may only be performed on a square matrix. After entering the matrix, select find inverse automatically. A new window will appear with the current matrix augmented by the appropriate identity. Reduce that new matrix until you get to the identity (or it is clear that you cannot) on the left hand side.  When you are finished, press the button in the input frame and the right hand side of the matrix will be isolated - if it can be found, and you reduced properly, this is the inverse.

                 Perform the Elementary Row Operations on a Matrix

                 Currently, only one of the elementary row operations is accessible directly by the user. That operation, swap rows, is available both to Tableaus and Matrices. Simply select it, and enter the two rows to be swapped in the inputframe. The other operations are available, but hidden to the user. Please email us if you see a need for them in the program - they are very easy to add.

                 Solve a System of Equations

                 To solve a system of equations, use an augmented matrix. Enter the equations in this matrix. Then, you may either reduce manually or use the automatic method. Most simply, after entering, select the solve-automatic command in the Matrix menu, and the solution will appear in a new window. Alternately, you may reduce it manually and then select solve-manual-print equations to see the solutions.

                 Solve the Dual Minimum Problem

                 To solve the minimum problem, you should use a tableau. Enter the system of inequalities (rewritten as equations with auxiliary variables) into a tableau. Then, you may either pivot manually and read the solution from the tableau, or you may choose the solve-minimum menu item and the solution will be presented to you in a new window.

                 Solve the Maximum Problem

                 To solve the maximum problem, you should use a tableau. Enter the system of inequalities (rewritten as equations with auxiliary variables) into a tableau. Then, you may either pivot manually and read the solution from the tableau, or you may choose the solve-maximum menu item and the solution will be presented to you in a new window.