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

$S_n=\{(x^{(i)},y^{(i)})$:$i=1,$dots,$n\},$ where $x^{(i)}in{R}^2$ and $y^{(i)}in\{1,-1\}.$

Suppose for a moment that we are able to find a linear classifier with parameters ${}^{\text{'}}$ and ${}_0^{\text{'}}$ such that

$y^{(i)}({}^{\text{'}}*x^{(i)}+{}_0^{\text{'}})>0$ for all $i=1,$dots,$n.$

Let hat$()$ and hat$({)}_0$ be the parameters of the maximum margin linear classifier, if it exists, obtained by minimizing

$\frac{1}{2}|||{|}^2,$ subject $to{y}^{(i)}(*x^{(i)}+{}_0)1$ for all $i=1,$dots,$n$

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 $S_n$ are linearly separable.