Answer and explain carefully please $($show how the maths was worked out$).$ Consider the following data set with $5$ vectors and $3$ variables:

$\backslash$table$[[$Vectors$,$x$^((1)),$x$^((2)),$x$^((3)),$x$^((4)),$x$^((5))],[$Variable $1,1,2,-1,-3,2],[$Variable $2,1,4,4,-2,-2],[$Variable $3,0,3,1,-1,0]]$

Treat all vectors as one cluster, $C,$ and compute the centroid and inertia of $C.$