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MATRICES HELP

Two square matrices (Dimension range : 2-10) can be added, subtracted, and multiplied together. The solution to the equation Ax = b, where A is a square matrix, x represents the matrix of variables x1,x2 etc. and b represents the matrix of solutions to the equation, hence the variables x1,x2 etc can be solved using the Jacobi iteration method (only for Matrix 1).The second matrix can be predefined by selecting the matrix buttons

Menu Location :- Tools > Equations > Matrices

Method :-

Enter a dimension of the matrix required (i.e. Enter a value for the Matrix Type field), press the okay button.

A matrix of input boxes will appear, of the required dimension.

Enter the numbers in each box for matrix 1.

For matrix 2 , Click the Matrix2 button and either enter values for the Matrix or use a predefined matrix.

Operation Matrix :

The solution matrix is displayed by clicking the Operation Matrix button . Addition, Multiplication, Subtraction,Transpose 1, Transpose 2 :- Selection of anyone of these buttons performs the required operation on the two matrices, for the Selected Column. The result of the operation will be displayed.

Solving Equations :

Complete the Matrix 1. Click the Solving tab. Enter your estimates for each variable. I.e. if the matrix is a

3x3 matrix, then enter estimates for x1,x2 and x3. Enter the number of iterations to perform. Click the

“Calculate” button. Solutions for the last four iterations will be shown. Check the solutions by back

substitution into the equations and the variance in the solutions themselves. Using this method the solutions

are not always found. Try changing the estimates, number of iterations and the order of the “rows” of the

matrix.

Matrix 1 Button :-

In the case below a 3 dimensional matrix has been selected, with the Equation Equal Matrix selected. This allows the Matrix to be solved in the Equation Solved tab.

Okay, button :- Once pressed the required matrix dimension will be displayed in the Matrix 1 and Matrix 2 button displays

Reset, button :- Clears the current Matrix displayed.

Matrix 2 Button :-

Pressing the Matrix 2 button displays the Matrix 2 display as below.

The Matrix 2 can be either entered into manually or by selecting a Pre-defined Matrix.

Pre-defined Matrices

For any dimensional matrix :

Enter a value for a diagonal matrix in the input box provided and click the DMAT button and a diagonal

matrix will appear

For a 2 or 3 dimensional matrix :

Enter a value for the angle, in RADIANS, and then select the RCLOCK button and a matrix will appear.

The same will occur if the RANTI button is pressed and the RFLEX button.

All these matrices can be used with Matrix 1.

RCLOCK :- Rotational matrix clockwise direction. RANTI :- Rotational matrix anti-clockwise.

RFLEX :- reflection of the matrix.

Operation Matrix button :-

Addition, Multiplication, Subtraction :- Selection of anyone of these buttons performs the required operation on the two matrices, for the Selected Column.

Selected Column :- Allows selection of the required column for which the results are required for.

Apply :- Performs the required task.

Sequence :-

Select the required column.

Select the required operation.

Click the Apply button, results will appear for the selected column.

Solution Matrix Button:-

This button will present the display below and will allow the solution to be found for Matrix 1.

Method : Enter the guess, approximate values for x1,x2,x3 etc…..Enter the number of required iterations, Click the Calculate for Matrix 1 button.. Three or less solutions for each x value will be calculated and displayed. If each value for a corresponding x value is similar then the required solution is found. If each solutions is widely different then no solution has been found. If this is the case then try changing the initial guesses and increasing the No. of iterations.