Answer the following questions about this 12 × 12 matrix:

(a) What is the bandwidth?

(b) Assuming this system has a solution for a given vector b, are you guaranteed to have convergence using successive relaxation? Explain your answer.

(c) If you perform Gauss elimination with partial pivoting, what is the entry a⁽²⁾_3,2?

Transcribed Image Text:

A= 1 0 2 1 1 0 0 0 0 0 02 1 2 1 0 0 0 0000 249 22 0000000 0 0 10 3 2 1 4 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 3 2 1 0 0 2 0 0 0 0 0 0 0 5 2 3 4 0 0 0 0 0 0 0 0 4 3 0 3 0 0 0 0 0000000 30000 000000 4 8 6 100 0 0 0 0 0 0 1 2 1 2 0 0 0 0 0 0 22 31 0 0 3 3 0 0