diff --git a/NumPy Fundamentals.md b/NumPy Fundamentals.md
index de00d82..7a2c749 100644
--- a/NumPy Fundamentals.md	
+++ b/NumPy Fundamentals.md	
@@ -8,7 +8,7 @@ Slide 2: What is NumPy? NumPy is a powerful library for numerical computing in P
 import numpy as np
 ```
 
-Slide 3: Creating NumPy Arrays NumPy arrays can be created from Python lists or using special functions. Code Example:
+Slide 3: NumPy arrays can be created from Python lists or using special functions. Code Example:
 
 ```python
 # From a Python list
@@ -26,8 +26,88 @@ c = np.ones((3, 2))   # Create an array of ones
 d = np.random.rand(2, 2)  # Create an array of random values
 # Output will be different each time
 ```
+Slide 4: Creating numpy arrays of random values and sizes and other similar functions
+```python
+random_array = np.random.randint(0,10,size=(2, 3)) # Creates a random array of size 2x3 and values ranging from 0 to 10
+print(random_array)
+
+random_array = np.random.rand(1,10) # Gives an random array of desired size 1x10 and random values
+print(random_array) #Ex) [[0.94200759 0.78812449 0.22936564 0.30757089 0.28442394 0.49795422
+# 0.38306793 0.85061234 0.91607897 0.54049652]]
+
+random_int = np.random.randint( 1,100)
+print(random_int)  # Output will be a random integer between 1 and 99
+
+random_array = np.random.randn(2, 3) # Outputs a random array of normal distribution and desired size 
+print(random_array)
+
+# Generate random numbers from a uniform distribution between 0 and 1
+random_uniform = np.random.uniform(0, 1)
+print(random_uniform)  # Output will be a random number between 0 and 1
+
+sample = np.random.choice([1, 2, 3, 4, 5], size=3, replace=False)
+print(sample)  # Output will be a random sample from the list without repetition
+np.mean(sample)
+
+# Generate a random permutation of elements in an array
+permutation = np.random.permutation([1, 2, 3, 4, 5])
+print(permutation)  # Output will be a randomly permuted version of the list
+
+# Generate a random number from a binomial distribution (number of trials=10, probability of success=0.5)
+random_binomial = np.random.binomial(10, 0.5)
+print(random_binomial)
 
-Slide 4: Array Indexing and Slicing NumPy arrays can be indexed and sliced like Python lists, but with more flexibility. Code Example:
+arr = np.linspace(0, 1, 5)  # 5 numbers between 0 and 1
+print(arr)  # Output = [0.   0.25 0.5  0.75 1.  ]
+
+``` 
+Slide 5: Matrix operations with numpy 
+```python
+# Addition
+matrix1 = np.array([[1, 2], 
+                    [3, 4]])
+matrix2 = np.array([[5, 6], 
+                    [7, 8]])
+result_add = np.add(matrix1, matrix2)  # Or simply: matrix1 + matrix2
+# Output = [[ 6  8], [10 12]]
+
+#Matrix multiplication
+matrix3 = np.dot(matrix1 , matrix2)  # Or simply: matrix1 @ matrix2
+# Output = [[19 22],
+#            [43 50]]
+
+# Inverse of a matrix
+matrix = np.array([[1, 2],
+                   [3, 4]])
+inverse = np.linalg.inv(matrix) # its determinant should be non zero
+
+#You can add or subtract a scalar or a 1D array (row/column vector) to/from a matrix using broadcasting.
+scalar = 10
+result_scalar_add = matrix1 + scalar
+#Output = [[11 12]
+#          [13 14]]
+
+result_scalar_multiply = matrix1 * scalar
+# Output = [[ 2  4]
+#           [ 6  8]]
+
+
+# Transpose of a matrix
+matrix4 = np.array([[1, 2],
+                    [3, 4],
+                   [5, 6]])
+transpose_matrix = matrix.T
+#Original Matrix:
+#[[1 2]
+# [3 4]
+# [5 6]]
+
+#Transpose of the Matrix:
+#[[1 3 5]
+# [2 4 6]]
+```
+
+Slide 6: Array Indexing and Slicing NumPy arrays can be indexed and sliced like Python lists, but with more flexibility. Code Example:
 
 ```python
 a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
@@ -37,7 +117,7 @@ print(a[1:, :2])  # Output: [[4 5]
                   #          [7 8]]
 ```
 
-Slide 5: Array Operations NumPy provides a wide range of mathematical operations that can be applied to arrays elementwise or across entire arrays. Code Example:
+Slide 7: Array Operations NumPy provides a wide range of mathematical operations that can be applied to arrays elementwise or across entire arrays. Code Example:
 
 ```python
 a = np.array([1, 2, 3])
@@ -51,7 +131,7 @@ e = np.sum(a)  # Sum of all elements in the array
 # Output: 6
 ```
 
-Slide 6: Broadcasting NumPy's broadcasting feature allows arithmetic operations between arrays with different shapes. Code Example:
+Slide 8: Broadcasting NumPy's broadcasting feature allows arithmetic operations between arrays with different shapes. Code Example:
 
 ```python
 a = np.array([[1, 2, 3], [4, 5, 6]])
@@ -60,9 +140,14 @@ b = np.array([10, 20, 30])
 c = a + b  # Broadcasting: b is "stretched" to match a's shape
 # Output: [[11 22 33]
 #          [14 25 36]]
+
+d = a*b # Broadcasting allows b to be automatically "stretched" to match the dimensions of a
+# Output = [[ 10  40  90],[ 40 100 180]]
+
+
 ```
 
-Slide 7: Array Reshaping NumPy arrays can be reshaped to different dimensions without changing their data. Code Example:
+Slide 9: Array Reshaping NumPy arrays can be reshaped to different dimensions without changing their data. Code Example:
 
 ```python
 a = np.array([1, 2, 3, 4, 5, 6])
@@ -75,7 +160,7 @@ c = a.reshape(3, 2)  # Reshape to a 3x2 array
 #          [5 6]]
 ```
 
-Slide 8: Array Concatenation NumPy provides functions to concatenate arrays along different axes. Code Example:
+Slide 10: Array Concatenation NumPy provides functions to concatenate arrays along different axes. Code Example:
 
 ```python
 a = np.array([[1, 2], [3, 4]])
@@ -91,7 +176,7 @@ d = np.concatenate((a, b), axis=1)  # Concatenate along columns
 #          [3 4 7 8]]
 ```
 
-Slide 9: Conditions and Boolean Arrays NumPy allows you to apply conditions and create boolean arrays for advanced indexing and filtering. Code Example:
+Slide 11: Conditions and Boolean Arrays NumPy allows you to apply conditions and create boolean arrays for advanced indexing and filtering. Code Example:
 
 ```python
 a = np.array([1, 2, 3, 4, 5])
@@ -101,7 +186,7 @@ b = a[condition]  # Filter elements greater than 2
 # Output: [3 4 5]
 ```
 
-Slide 10: Mathematical Functions NumPy provides a wide range of mathematical functions to perform various operations on arrays. Code Example:
+Slide 12: Mathematical Functions NumPy provides a wide range of mathematical functions to perform various operations on arrays. Code Example:
 
 ```python
 a = np.array([1, 2, 3, 4])
@@ -113,7 +198,7 @@ d = np.sqrt(a)  # Compute square root values
 # Output: [1.         1.41421356 1.73205081 2.        ]
 ```
 
-Slide 11: Loading and Saving Arrays NumPy provides functions to load and save arrays from/to disk in various formats. Code Example:
+Slide 13: Loading and Saving Arrays NumPy provides functions to load and save arrays from/to disk in various formats. Code Example:
 
 ```python
 # Save an array to a binary file
@@ -125,7 +210,7 @@ b = np.load('data.npy')
 # Output: [1 2 3 4]
 ```
 
-Slide 12: NumPy and Data Analysis NumPy seamlessly integrates with other data analysis libraries like Pandas and Matplotlib, making it an essential tool for scientific computing and data analysis in Python. Code Example:
+Slide 14: NumPy and Data Analysis NumPy seamlessly integrates with other data analysis libraries like Pandas and Matplotlib, making it an essential tool for scientific computing and data analysis in Python. Code Example:
 
 ```python
 import pandas as pd
@@ -139,3 +224,22 @@ plt.plot(x, y)
 plt.show()
 # Displays a line plot using the NumPy arrays x and y
 ```
+ Slide 15: Indexing rows, columns, sub-matrices:
+ ```python
+m =  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+m[0,2] # Outputs 7 (item index (1,3) for mathematiicans)
+
+m[[0,2]] # Will retrieve the first and third rows:
+# Output = [[1, 2, 3],
+#           [7, 8, 9]]
+
+m = [: , [1,2]] # Will retrive second and third columns:
+#Output = [[2, 3],
+#          [4, 5],
+#          [8, 9]]
+
+m[[0,2]][:,[1,2]] #Outputs a sub-matrix with first and third rows and second and third columns:
+# Output = [[2, 3],
+#           [8, 9]] 
+```
+