3)For the linear system Ax=b where A=[ 6 , -8 ; -15 , 1 ] and b= [ 1 ; -35 ] a)

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3)For the linear system Ax=b where A=[ 6 , -8 ; -15 , 1 ] and b= [ 1 ; -35 ]

a) Is the matrix A strictly diagonal dominant? Why?

b) If your answer to the previous question is YES, will Jacobi's method converge for any initial condition? If your answer to the previous question is NO, how can this system be modified so that Jacobi's method will converge?

4) Consider solving Ax=b by iterative method

x^(k+1)=T(^-1) S X^(k) + T^(-1) b

where T^(-1)S is the iteration matrix. Let B,C, and D be the iteration matrices corresponding to 3 different iterative methods. The eigenvalues of B (method 1) are 0.01, 0.05, & -1.01. The eigenvalues of C (method 2) are 0.1, 0.1, -0.9. The eigenvalues of D (method 3) are -0.4, -0.5, & -0.6.

a) Which method(s) converge(s) to the solution? Why?

b) Which method do you think converges fastest? Why?

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