Derive the Closed$-$Form of Linear regression using matrix notation $($as discussed in class on $9^{th}$ Feb$).$

Explain the rules used at every step. $(30$ marks$).$

Hint: For finding the value of $$ that minimizes $J()$ in closed$-$form start with matrix representation of $J.$

$gra{d}_{}J()=gra{d}_{}\frac{1}{2}(x-$vec$(y){)}^T(x-$vec$(y))$