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Solve each item supporting your answer with clear explanation. 1.Consider the following augmented matrix of a system...

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Advance Math

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]?

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