$($a$)$ A portfolio with three securities $a_1,a_2,a_3$ with expected returns, ${}_1=20\%,{}_2=13\%,{}_3=4\%,$ standard deviations of returns, ${}_1=25\%,{}_2=28\%,{}_3=20\%,$ and the correlation between returns, ${}_{12}=0\mathrm{.}3,{}_{13},=0\mathrm{.}15$ and ${}_{23}=0\mathrm{.}4.$ If risk free interest rate is $10\%$ then compute the weight vector for market portfolio.