= Solution
A <separating hyperplane> for signed data satisfies $Y_i(\gamma_0+X_i^T\beta)>0$ for every $i$; its geometric set is $\{x:\gamma_0+x^T\beta=0\}$. The plot marks three <support vectors>. At the shown fit they lie on the two <support-vector-machine margin boundaries>, so their signed functional margins satisfy
$$
Y_iX_i^{*T}\widehat\gamma=1.
$$
The solid line is the decision hyperplane $X^{*T}\widehat\gamma=0$, while the dashed parallel lines are $X^{*T}\widehat\gamma=1$ and $X^{*T}\widehat\gamma=-1$.
If $\lambda=0$, every parameter vector with all margins at least one has zero hinge loss. Scaling or changing a separating vector can therefore give another minimizer, so the objective need not select the displayed maximum-margin direction or the same three lines. Positive quadratic regularization selects a finite, minimum-norm compromise.
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