$1.(1)$

$2\mathrm{.}5$ points possible $($graded$,$ results hidden$)$

Consider a classification problem where we are given a training set of examples and labels $,$ where and $.$

Suppose for a moment that we are able to find a linear classifier with parameters and such that for all $.$

Let and be the parameters of the maximum margin linear classifier, if it exists, obtained by minimizing

Determine if each of the following statements is True or False. $($As usual, $$True$"$ means always true; $$False$"$ means not always true.$)$

The minimization problem defined by the equation immediately above has a solution if and only if the training examples are linearly separable.