Provide mathematical solution and answer not in python code.

SVM$.$ An SVM classifier is trained on $44$ images, $x_i$ with binary labels $y_i=+-1.$ Three of

the images in the training data set are:

$x_1=\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 0& 0& 0\\ 1& 0& 0& 0\\ 1& 0& 0& 0\end{array}\right],x_2=\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 1& 0& 0\\ 0& 1& 0& 0\\ 0& 1& 0& 0\end{array}\right],x_3=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 1& 0\\ 0& 0& 1& 0\\ 0& 0& 1& 0\end{array}\right],$

with labels $y_1=1,y_2=1,y_3=-1.$ You are given a test image,

$x=\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 0& 0& 0\\ 0\mathrm{.}5& 0\mathrm{.}5& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

$($a$)$ The training and test images, $x_i$ and $x,$ are converted to $16-$dimensional vectors $x_i$ and

x$.$ Find the squared distances

$d_i=||x-x_i|{|}^2,i=1,2,3.$

$($b$)$ Suppose a kernel is

$K(x,x_i)=$max$\{0,1-||x_i-x|{|}^2\}.$

What value of $>0$ guarantees that $K(x,x_i)>0$ for $y_i=1$ and $K(x,x_i)=0$ for $y_i=-1$

for $i=1,2,3.$