Quick Guide to MAT
|| Running
MAT
|| Main
Menu
|| Entering
Matrices
|| Matrix
Editing
|| Matrix
Handling
|| Matrix
Operations
|| Tutorials || Algebraic
Expressions
|| Matrix
Archive
 
Click on the symbol in the text, to get back to the top of the page.

What is MAT?

MAT is Microsoft Windows software for teaching matrix operations and applications. MAT's extremely simple Windows interface and its step by step tutorials, facilitate the teaching and learning of matrix operations and its applications.

back to the top  Running MAT:

MAT is accessed through ASP's main screen, by clicking on the "to MAT" title below the outline border of the graphic pane. By this action, the user is prompted with MAT's main screen, which covers the entire screen space.

how to access MAT

MAT was designed to efficiently utilize the screen space so as to handle and visualize large matrix expressions, and as such, there are no buttons or control panel that could occupy any screen real estate. All options and tools are available by accessing "hidden menus" which are prompted by left or right mouse button clicking on certain regions of the screen.

back to the top  The Main MAT Menu:

MAT's general menu, is prompted to the user by LEFT mouse button clicking on any location of the blank screen where just background is present. This menu includes the following options:

ExitTo exit MAT going back to ASP's main screen.
HelpTo access this help pages.
Add Expression Allows the user to access the Matrix editing window to enter a matrix by typing or by accessing the archive of matrices created by the user.
Edit To edit a selected matrix expression from those present on the screen. The selected matrix should have any of its elements highlighted. If no matrix has been selected, the last typed matrix would be edited.
Delete Selected Expression To delete from the screen a selected matrix. A matrix is selected when any of its elements is highligted.
Delete All Expressions Erases ALL matrices from the screen, leaving it blank.
Compact MAT Space To position the matrix expressions left on the screen with minimal basic spacing in between. Mainly used when some matrices have been deleted from the screen, leaving unused spaces.
Gen Audit Trails When this option is checked, MAT will keep all original matrix expressions on the screen, even after matrix operations have been performed within the matrices.
Select Colors To access the color palettes for the general screen display.

back to the top  Entering Matrices : This is done by clicking on "Add Expression" from the general menu. This action prompts the user with the Matrix editing window. This window consists of an upper box where the user types the elements of the matrix, and a lower window, where the matrix as interpreted by the program, is displayed.

MAT handles:

The typing of all matrices should start with an openning square bracket "[", and should end with a closing square bracket "]". The elements are typed row by row, starting with the top one. The different elements of the row should be separated by commas ",". The starting of a new row is indicated by a semi-colon ";".

back to the top  Standard Matrices:
Example:
To enter the matrix

The user types: [3,4,0,2;-2,1,5,-3;0,-1,6,-4] . When finished typing, the key "Enter" should be pressed or the button Done should be clicked.

The following picture illustrates the details of the matrix editing window:

back to the top  Augmented matrices :
MAT allows the user to enter "augmented matrices" to use in the Gauss-Jordan diagonalization method for solving systems of equations. For example, to enter the augmented matrix for the system of linear equations:

The user types: [1,1,1|3;2,3,1,5;1,-1,-2,-5] . Where the "vertical bar" that separates the coefficients that accompany the variables, from the "pure numerical values" on the right hand side of the equations, is specified by the vertical bar key "|", instead of the comma. To specify that an augmented matrix is being given, only one vertical bar may be used while entering the first row of elements. There is no need to repeat this for the rest of the rows, and commas may again be used to delimit elements. When finished typing, the key "Enter" should be pressed or the button Done should be clicked.

The details in the editing window are shown in the following picture:

back to the top  Simplex Tableaux:
Simplex Tableaux for linear programing problems can also be entered, since MAT offers step by step tutorials on the Simplex method. The row corresponding to the objective function should be separated from the rows representing the constraints for the problem, by the use of a horizontal line separator. The objective row should always be entered as the last row.

For example, to enter the Simplex Tableau for the following problem:

The user types: [2,5,1,0,0|58;-1,1,0,1,0,-15_-20,-70,0,0,1,0]. Where the "underscore" symbol "_" instead of the semicolon, indicates that the next row is the objective row.

The tableau displayed by MAT will look as follows:

back to the top   Matrix Archive:
The matrix editing window allows the user to archive the matrix that was just typed, by simply clicking on the button : Add to Archive. All the matrices stored in said archive, can be accessed and brought to the screen for future use. While in the matrix editing window, any matrix stored in the archive can be retrieved by pressing the View Archive button and clicking on the selected matrix expression listed in drop-down menu of the archive, and using the option Use Selected.

back to the top   Editing Matrices:

The simplest and quickest way of changing the values of elements in a matrix is by right mouse button clicking on the element to be changed and by using the up/down arrows on the spin control window that is prompted, to increase/decrease the numerical values.

If the changes involve the typing of algebraic expressions or if the actual dimensions of the matrix have to be modified, the editing box for the particular matrix should be accessed. This is done through:
 
(a)   The general MAT menu (accessed by left mouse button clicking on the background) - option: Edit Expression (an element in the relevant matrix should be previously highlighted to indicate which is the selected matrix, otherwise the very last matrix entered would be edited).
 
(b)   The matrix handling menu for the matrix (accessed by right mouse button clicking on the region of the screen limited by the matrix's OPENING bracket) - option: Edit Matrix

Once the editing window is accessed, the relevant changes should be made on the edit box (upper part of the window), and the changes would be instantly refreshed on the lower part of the window. When the changes are done, the "Enter" key should be pressed or the Done button clicked.

The Hidden Menus :

Once at least one matrix is displayed on the MAT screen, two other menus can be accessed by the user. One gives the user options on general handling of a particular matrix, and the other one shows options with reference to different operations to be performed within the matrix, these include diagonalization, calculation of the determinant for a square matrix, transposition, simplex method for a simplex tableau, raw and column multiplication by scalars, addition or subtraction of columns or rows, etc.

Depending on where on the screen the user clicks, and with which mouse button, the diferent menus will pop up. When a matrix is displayed on the screen, new "clicking spaces" are defined. This is illustrated in the following picture:

back to the top Matrix Handling Menu

It is accessed by RIGHT mouse button clicking on the opening bracket area of the matrix of interest. The menu options are:

Edit ExpressionTo access the editing window for the matrix.
Delete ExpressionTo delete from the screen the matrix expression.
Clone Expression Creates an exact duplicate of the matrix on the screen.
Add Expression to Archive Copies the matrix expression to the matrix archive for future use.
Expression Audit Trail When this option is checked (by clicking on it) a copy of the original matrix expression is kept on the screen even after matrix operations have been performed.

back to the top Matrix Operations Menu

It is accessed by RIGHT mouse button clicking on the closing bracket area of the matrix of interest. This menu offers operations within a unique matrix expression. The menu options are:

Diagonalize Matrix Performs the diagonalization of the matrix (ideal for Gauss-Jordan method using augmented matrices). This can be done in ONE step by clicking on the sub-option: Just Do It, or through a step-by-step tutorial, by clicking on the Animate sub-option.
Transpose Creates the transpose of the given matrix
Evaluate Simplex Only shown (available) when the matrix in question is in Simplex Tableau form. Performs the Simplex maximization method in ONE step (by clicking on Just Do It, or through the step-by-step tutorial (by clicking on the Animate sub-option)
Compute Determinant Computes the determinant of a SQUARE matrix. Nothing will be performed if the matrix in question is not a square matrix.
Scale Row Multiplies the user's selected row by a scalar, throught an interactive dialog process.
Scale Column Multiplies the user's selected column by a scalar, throught an interactive dialog process.
Exchange Rows Exchanges the rows selected by the user using interactive dialog boxes.
Exchange Columns Exchanges the columns selected by the user using interactive dialog boxes.
Subtract Rows Subtracts a row multiplied by a given scalar, from another row, using dialog boxes.
Subtract Columns Subtract a column multiplied by a given scalar, from another column, using dialog boxes.

Operations Between Matrices:
 
Addition, subtraction and multiplication of matrices should be typed as such when adding a new expression. Some examples follow:

To add the matrices:

after accessing the edit window through the Add Expression option in the main menu, the addition is typed in the edit box as shown in the following figure:

The operation will appear on the MAT screen as follows:

To multiply the matrices:

after accessing the edit window through the Add Expression option in the main menu, the multiplication is typed in the edit box as shown in the following figure:

The operation will appear on the MAT screen as follows:

back to the top  Tutorials :

MAT offers tutorials for lengthy or complicated methods, to facilitate the teaching and learning of the subject. Tutorials are available for Gauss-Jordan diagonalization and for the Simplex method. Once the appropriate matrix, augmented matrix or Simplex tableau has been typed by the user, when accessing either Diagonalize Matrix or Evaluate Simplex, two sub-options are available. These are: Just Do It, or Animate. The step-by-step tutorials are accessed by clicking on the Animate option. Once in the "Animator" window, the user advances step by step clicking on the One Step button. The Animator window shows what the next step would be and the result of each step.

The following figure illustrates one step in a Simplex evaluation:

back to the top  Algebraic Expressions :

MAT allows the use of generic algebraic notation to demonstrate basic properties of operations between matrices. Characters can be entered as matrix elements instead of numerical values, and the resulting operations to be performed will be shown on the MAT screen.

For example, to illustrate the multiplication of a generic (2 x 3) matrix by a generic (3 x 2) matrix, the following can be entered through the Add Expression option of the main menu:

The result of the multiplication is shown on the MAT screen as follows: