Q$2(40$ pts$)$: Support vector machines learn a decision boundary leading to the largest margin from both classes. You are training SVM on a tiny dataset with $4$ points shown below. This dataset consists of two examples with class label $-1($denoted with plus$),$ and two examples with class label $+1($denoted with triangles$).$

Questions:

$($a$)$ Write down the SVM loss function for this data and state how to find the weight vector w and bias b $.[10$ points$]$

$($b$)$ Draw the $($approximate$)$ decision boundary. $[20$ points$]$

$($c$)$ What are support vectors in this dataset? $[10$ points$]$

Proof: