$($a$)$ Consider the following dataset: $A1\frac{2,10}{?}$ Class $,11)/$Class C$3,$ A$4(6,9)/$Class C$2.$ In the above dataset, we have four data points with three class labels. Applying the KNN algorithm $(K=3),$ find the class label of the point $P(5,7).$ Numbers within parentheses are coordinates.

$($b$)$ Given a linear regression model $Y=W^{T}x+$ with the following information. The initial weight vector: $W=[2,3,7,5{)}^T$; Input training sample: $x=[5\mathrm{.}6,6\mathrm{.}8,4,8{]}^T$; Bias: $=[1\mathrm{.}2,1\mathrm{.}3,2\mathrm{.}2,1\mathrm{.}5{]}^T$ and Training output: $Y=[y_{01},y_{02},$dots,$y_{a4}{]}^T.$ Assuming that the loss function as $L(RMSE)$ to be minimum, find the values of $Y$ vector, given that the model is trained till first pass only. $[$RMSE $=$ Root Mean Square Error