Q$3.$ Consider a weighted linear model fitting problem

$mi{n}_x{\displaystyle \underset{i=1}{\overset{n}{}}}{w}_i(y_i-a_i^{T}x{)}^2,$

where $w_1,$dots,$w_n$ are nonnegative weights corresponding to the data pairs $(y_i,a_i)$ for $i=1,$dots,$n.$

Derive the solution of this fitting problem using i$)$ projection theorem and ii$)$ convex optimization's

optimality condition $($verify that the function to be minimized is convex in $x$ first$).$

$(10\%)$