The variance$-$covariance matrix of returns for $3$ risky stocks is given below:

$($a$)$ Find the global minimum variance portfolio for the $3$ risky stocks, assuming short selling

is allowed. Show your steps.

$($b$)$ Repeat part $($a$),$ assuming short selling is not allowed. Show your steps.

$($c$)$ Check that the Kuhn$-$Tucker conditions in part $($b$),$ if any, are satisfied.