Given a $2-$input $1-$output RBF network with two RBF centers at T$1=[0,0]$ and T$2=[1,0]$ with two weights w$1$ and w$2,$ and one bias w$0,$ four input vectors X$1=[0,0],$ X$2=[0,0\mathrm{.}9],$ X$3=[1,0],$ X$4=[1,0\mathrm{.}9]$ with the corresponding desired output vector D$=[1,0,0,0],$ and the Gaussian function consisting of the squared l$2-$norm operator is used as the radial basis function.

Show the step$-$by$-$step calculation to obtain the combined weights $[$w$0,$w$1,$w$2]$ to recall the four corresponding outputs Y$1,$ Y$2,$ Y$3,$ Y$4$ and submit the sum of the $3$ weight values as Your Answer by typing its numerical value $($rounded to $4$ decimal places$)$ into the Answer Box below. Hint: A minimum resolution of $6$ decimal places for step$-$by$-$step calculation is required.

please show mathetetical steps for the sums.