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               Here, we use Scalar multiplications in different ways. Let us try three methods listed as follows.. ·        1D array scalar multiplication ·        2D array scalar multiplication ·        Different scalars for each column The sample code is given below. 1D array scalar multiplication:   This code multiplies the array by 3. First, it creates an array of elements. Each element is multiplied by 3. The result is displayed. Code: import numpy as np1 # Create an array with elements s_arr = np1.array([1, 3, 5, 7, 9, 11, 13, 15]) # Scalar multiplication by 3 result = s_arr * 3 print("Original array:", s_arr)    print("Multiplied by 3:", result) Output: Original array: [ 1   3   5   7   9 11 13 15] Multiplied by 3: [ 3   9 15 21 27 33 39 45] 2D array scalar multiplication: ...

              Array is a collection of similar data elements. When you implement the arithmetic operations, you have to do each element. Let us implement this as follows. Element-wise Arithmetic Operations in Numpy:               It starts from importing numpy library. First, two arrays are included as input. Element wise operations are performed and result is printed. Code: import numpy as np1 # Two arrays as input s_arr1 = np1.array([11, 22, 33, 44]) s_arr2 = np1.array([5, 10, 15, 20]) # Arithmetic operations on element wise print("Element wise Arithmetic Operations:") print("Addition:", s_arr1 + s_arr2)         print("Subtraction:", s_arr2 - s_arr1)      print("Multiplication:", s_arr1 * s_arr2)   Output: Element wise Arithmetic Operations: Addition: [16 32 48 64] Subtraction: [ -6 -12 -18 -24] ...

               Indexing is the process of retrieving specific elements, whereas slicing extracts subarrays in a range. Both methods support negative indices and returns the original array elements. Mainly, these two methods make the user to access, extract the elements and manipulates the array in efficient manner. Let us discuss the methods with sample code as follows… Indexing in Numpy:               It supports three methods as follows. ·        Single element indexing ·        Multi-dimensional indexing ·        Index arrays The sample code is given below.. Single element indexing:               It follows list concept in python. Code: import numpy as np1 s_arr = np1.arange(10)    # [0,1,2,3,4,...

       Numpy has attributes for arrays. These attributes describes the structure and the content. These are given below… ·        .dtype ·        .shape .dtype:               It means ‘data type’. It gives the information about the values to be stored in the array. eg. Integers,floats,strings. .shape:               It provides the dimensions of the array. It may be of single dimensional, two dimensional or three dimensional. Let us create python program to implement using Numpy. Sample Python Numpy code for .dtype: # Example 1: Integer array Import numpy as np s_int = np.array([11, 22, 33, 44]) print("Array Elements:", s_int) print("Data type of the Array is:", s_int.dtype) Output: Array Elements: [11 22 33 44] Data type of the Array is: int64 #...

              ‘Numpy’- a python library which holds many built-in functions specially designed for scientific computing. It is efficient for multidimensional arrays. It supports data science, machine learning. It provides the following features. ‘ndarray’- it supports N-dimensional array. Automatic alignment can be done. Operations are vectorized. It supports many libraries. High performance is achieved. Let us follow the steps to import and install the Numpy in your system. First, open the command prompt or terminal In windows: search tab, type Command Prompt. Other Os like macOS/Linux: open the Terminal. Next, run the pip command with Numpy keyword. C:\Users>python -m pip install numpy It successfully install your Numpy. Once, it was successfully installed, check it with following code. C:\Users>pip list Package             Version ------------------ ------...

               Let us compute the determinant of a matrix using the Numpy Library. How to find determinant of a matrix in mathematical way?               It is a scalar value that deals with a square matrix. It is denoted by det(A) or |A|. If it is a 2×2 matrix, it follows this formula. For A=[abcd], the determinant is |A|=ad−bc. If it is a 3x3 matrix, it uses /laplace expansion or cofactor method. If you have nxn matrix, it uses Leibniz formaula,Laplace expansion or Gaussian elimination. Let us implement in three ways. 1.       Normal method. 2.       Using Numpy 3.       Using Laplace 1.Normal method.               This method uses the simple code implementation. Code: # 2x2 determinant without NumPy def det_2x2(s_ma...