$9\mathrm{.}23$ Write a MATLAB program for minimizing the two$-$weight mean squared error $($MSE$)$ function

$J=100+100w_1^2+4w_2^2-100w_1-8w_2+10w_1{w}_2$

by applying the steepest descent algorithm for $500$ iterations.

The derivatives are derived as

$\frac{dJ}{d{w}_1}=200w_1-100+10w_2$ and $\frac{dJ}{d{w}_2}=8w_2-8+10w_1$

and the initial weights are assumed as $w_1(0)=0,w_2(0)=0,=0\mathrm{.}001.$

Plot $w_1(k),w_2(k),$ and $J(k)vs.$ the number of iterations, respectively, and summarize your results.