3. Consider the linear system of the boundary value problem discussed in the last problem, i.e. vj1+2vjvj+1+2vj=22sin(xj), forj=1,2,,N1, (3) h2 whereh=1/N,vj istheapproximationtou(xj)forj=1,2,,N1,andv0 =vN =0.

(a) Implement Jacobis iteration method to find an approximation of the solution to (3) using a stopping criterium of ||b Ax(k)||

(b) Repeat (a) for the Gauss-Seidal iteration.

PLEASE DO PART B WITH GAUSS-SEIDAL. PLEASE LOOK AT THE ORIGINAL EQUATION AND WRITE PYTHON CODE BASED ON THAT. THANK YOU!

3. Consider the linear system of the boundary value problem discussed in the last problem, .e. N -1 -Ui-1 h2 ,N-1, and vo = UN = 0. where h = 1/N, ui is the approximation to u(x) for j = 1,2, (a) Implement Jacobi's iteration method to find an approximation of the solution to (3) using a stopping criterium of lib-Ax(