Solve each item supporting your answer with clearexplanation.
1.Consider the following augmented matrix of a system of linearequations.
( 7 −3 4 6
−3 2 6 2
2 5 3 −5 )
a. Solve the system with the Jacobi method. First rearrange tomake it diagonally dominant if possible. Use [0,0,0] as thestarting vector. Find the condition number of the matrix ofcoefficients κ∞(A), and compute how many iterations arerequired to get the solution accurate to five significantdigits?
b. Repeat part a) using the Gauss-Seidel method. Are feweriterations required?
c. Is convergence faster in parts a) and b) if the startingvector is [-0.26602, -0.26602,-0.26602]?
