$2.$ Consider the following training data

$($a$)$ Plot these six training points. Are the classes $\backslash (\backslash \{+,-\backslash \}\backslash )$ linearly separable?

$($b$)$ Construct the weight vector of the maximum margin hyperplane by inspection and identify the support vectors.

$($c$)$ If you remove one of the support vectors does the size of the optimal margin decrease, stay the same, or increase?

$($d$)$ Is your answer to $($c$)$ also true for any dataset? Provide a counterexample or give a short proof