The problem has 3 classes and 4 input features. The possible classes are (B: balanced, L: left, R: right), and the 4 input features are: (LW: left weight, RW: right weight, LD: left distance, RD: Right distance). The balance shows up the value B when LW + LD = RD + RW. Each raw of the file data is constructed as the following: Class, LW, LD, RW, RD. Example: B, 3, 2, 4, 1. In addition, all the input features might have values 1, ..., 5. For more information refer to website given before. Remark: you are free to propose a preprocessing of the input features, also youre advised to try different values of the learning rate and observe the training curve. Remark: in your code, you are asked to use python, numpy and matplotlib. You shouldnt use libraries like scikit, tensorflow, pytorch, or any other library dedicated to AI. Remark: Provide an intelligible and commented algorithm that shows your deep understanding of your code. Remark: as far as the normalized algorithm is concerned, it is usual to prevent a possible division by zero, so a small real positive number is added to the divisor.

Exercise 1: Let's first study the simple problem in which only 2 classes (R: Right, E: else) are observed. The balance shows up either C1 (R), when RW + RD > 3 or C2 (E) otherwise. The problem now has only two input features RW and RD. 1- Write a function to create the new data set. 2- Write a function to plot the patterns relatives to classes R and E in different colors and different shapes. Is the problem linearly separable? Give an explanation. Remark: you can include the figure and your response into a markdown cell or provide them in a separate pdf file