How can I define a 3D matrix in MATLAB? 

For example a matrix of size (8 x 4 x 20) or add a 3rd dimension to an existing 2D matrix? 

Answers:  

A 3D matrix, also known as a 3-dimensional array, can be created in various programming languages such as Python, C++, and MATLAB. In Python, you can create a 3D matrix using the Numpy library. To install Numpy, you can use the following command: 

pip install numpy

Once Numpy is installed, you can create a 3D matrix using the following code: 

import numpy as np
matrix = np.array([[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]]])

In this example, we create a 2x2x3 matrix, meaning it has 2 layers, each with 2 rows and 3 columns. The elements in the matrix are assigned values ranging from 0 to 11.

In C++, you can create a 3D matrix using nested loops and arrays. For example, you can create a 3x3x3 matrix as follows: 

#include 
using namespace std;

int main() {
    int matrix[3][3][3];
    for(int i = 0; i < 3; i++) {
        for(int j = 0; j < 3; j++) {
            for(int k = 0; k < 3; k++) {
                matrix[i][j][k] = i + j + k;
            }
        }
    }
    return 0;
}

In this example, we use three nested loops to initialize the elements of the 3D matrix. The elements are assigned values equal to the sum of their indices.

In MATLAB, you can create a 3D matrix using the cat function or by directly assigning values to a multidimensional array. For example: 

matrix = cat(3, [1 2 3; 4 5 6], [7 8 9; 10 11 12])

This code creates a 2x2x2 matrix, where the first and second layers are 2x3 matrices.

In conclusion, creating a 3D matrix in various programming languages involves understanding the syntax and functions specific to the language, as well as the basic concepts of arrays and matrices.