Please answer the following questions about the Support Vector Machine.

$($a$)$Assume the hard$-$margin SVM is used. If we know that the data points $(2,-1),(0,1),(-4,3)$ with labels $-1,1,1$ are the support vectors, please derive the decision boundary of the SVM$.$

$($b$)$ Please tell the difference between soft$-$margin SVM and hard$-$margin SVM and explain why soft$-$margin SVM typically reveals better results than the hard$-$margin SVM$.$