In: Advanced Math
Solve each item supporting your answer with clear explanation.
1.Consider the following augmented matrix of a system of linear equations.
( 7 −3 4 6
−3 2 6 2
2 5 3 −5 )
a. Solve the system with the Jacobi method. First rearrange to make it diagonally dominant if possible. Use [0,0,0] as the starting vector. Find the condition number of the matrix of coefficients κ∞(A), and compute how many iterations are required to get the solution accurate to five significant digits?
b. Repeat part a) using the Gauss-Seidel method. Are fewer iterations required?
c. Is convergence faster in parts a) and b) if the starting vector is [-0.26602, -0.26602,-0.26602]?