Answer this with and without the threshold, show all the workings $($maths$)$ and explain clearly $($please also draw the resulting graph$)$Reconsider the set with $6$ examples and the following distance matrix $($for some choice of distance function$).$

$\backslash$table$[[,$x$^((1)),$x$^((2)),$x$^((3)),$x$^((4)),$x$^((5)),$x$^((6))],[$x$^((1)),0,0\mathrm{.}20,0\mathrm{.}15,0\mathrm{.}76,0\mathrm{.}54,0\mathrm{.}31],[$x$^((2)),0\mathrm{.}20,0,0\mathrm{.}89,0\mathrm{.}18,0\mathrm{.}66,0\mathrm{.}27],[^((3)),0\mathrm{.}15,0\mathrm{.}89,0,0\mathrm{.}82,0\mathrm{.}73,0\mathrm{.}56],[$x$^((4)),0\mathrm{.}76,0\mathrm{.}18,0\mathrm{.}82,0,0\mathrm{.}42,0\mathrm{.}39],[$x$^((5)),0\mathrm{.}54,0\mathrm{.}66,0\mathrm{.}73,0\mathrm{.}42,0,0\mathrm{.}51],[$x$^((6)),0\mathrm{.}31,0\mathrm{.}27,0\mathrm{.}56,0\mathrm{.}39,0\mathrm{.}51,0]]$

Use Hierarchical clustering but impose a threshold of $0\mathrm{.}35$ on the inter$-$cluster distance. Write the final clusters.

Use Hierarchical clustering but impose a threshold of $3$ on the number of clusters. Write the final clusters.

Use single linkage as the inter$-$cluster dissimilarity metric.