Matrix Algebra Operations

Matrix Addition

Two 6-sided dice are rolled. What is the most probable outcome?

Select Matrix

and click on the Enter Data command

Change Matrix Dimensions (Rows, Columns) from 2,2 to 6,1 and click on the Define Frame command

Enter numbers 1 2 3 4 5 6 and on the Enter Data into Matrix select 1. A red square will appear right on the View line

Click on the red square

Click on the Transpose command. The Select an operand message will appear toward the bottom left of the matrix module. Click on 1. A message Select matrix cell to which deposit the result will appear. Click on the Results 2 command. A second red square will appear. Click on the second red square command.

Select the ( Addition, Matrices ) X + Y command. A Select two operands message will appear. Click on the Operands 1 and the Operands 2 commands. A message Select matrix cell to which deposit the result will appear. Click on the Results 3 command. A third red square will appear. Click on the third red square command.

The most likely outcome is 7. The probability that, when throwing 2 dice, the outcome will be 7 is thus 6/36 = .1667. To compute probabilities of other outcomes, Transfer Matrix 3 to the vector display, select ( Reshape, Decompose ) , decompose matrix into a column vector and select ( Frequencies, Proportions )

Note that the sum of probabilities of all possible outcomes equals 1.00. To visualize these outcomes, select ( Graphs, Histograms )

Matrix Subtraction

Variance of numbers 1 2 3 4 5 is 2.00

To show that variance is the average number of all possible differences between values of a variable, open the Matrix module, and transfer the variable X into the matrix module by clicking the ( Transfers, Vectors-Matrix) commands.  Depositing the variable X into the Matrix 1. Click on the Transpose command, select the Operand, and store the transposed variable X in the Matrix 2.  Click on the Unfold command. Select the ( Delta X ) command, select Operands 1 and 2, and store the result in the Matrix 3. Click on the red square corresponding to Matrix 3.

Select the X^2 command ( Operand 3, Results 4 ) and click the red square corresponding to the Matrix Cell 4.

Select ( Means, Matrix 4, Enter the Grand Mean into the Matrix Cell 5 ). Label and display the Matrix Cell 5, containing the variance of the Variable X.

Visualize Distributions in the 3-D

Select ( Arguments, -3 to +3 Intervals ), select the n=13 Interval, click on the Generate command and the Display the Sequence command. Replace the data on the vector display. Select ( Distributions, Ordinates of Normal Distribution, mark the Argument , and click on the Accept command.

Select ( Data, Delete )

select Argument Z, and click on the Clear and Compact command. Open the Matrix module, select ( Vectors-Matrix, Matrix 1 ), Click Transpose, save the transposed matrix in the Matrix 2, click on the Matrices  X+Y command, and store the resulting matrix in the Matrix Cell 3.

Select the Transfer command and click on the Matrix Cell 3.

Repeat the previous steps, but instead selecting the  X+Y command in the matrix module, select the X*Y command. Transfer the resulting matrix to the vector module and click on the Stereoimages command.

You can view the rotated distribution as