What is the goal of the SVM algorithm? When can be it successfully applied?$$What linear function is used by a SVM for classification? How is an input vector xi $($instance$)$ assigned to the positive or negative class?$$If the training examples are linearly separable, how many decision boundaries can separate positive from negative data points? Which decision boundary does the SVM algorithm calculate? $$For many real life data sets the decision boundaries are not linear. How is this non$-$linearity dealt with by SVMs$?$Consider the three linearly separable two$-$dimensional input vectors in the figure on the right. Find the linear SVM that optimally separates the classes by maximizing the margin.