Answer is B or C but I am having difficulty determining if this is ill condition

Question

Answer is B or C but I am having difficulty determining if this is ill conditioned or well conditioned. Please give a full explination as to why it is one or the other.

I. In solving the system of equations, [A]fx) b 5 11(1 if the inverse of the coefficient matrix is 0.231 0.077 0.154 0.385 The conditioning number of the matrix [A] using the Loo norm is (a) not computable because A-1 has negative entries. (b) K(A)-3.231, the system is well conditioned, and small residuals mean an accurate solution has been obtained. (c) K(A)-3.231, the system is ill-conditioned, and small residuals mean an accurate solution has been obtained. (d) K(A)=591,267.25, the system is ill-conditioned and small residuals do not mean accurate solution has been obtained none of the above (e)

Explanation / Answer

Option B is correct

If the condition number is very small, then the matrix is said to be well-conditioned.

condition number of matrix ||A|| ||A-1||

||A|| = max ((5+1) ,(2+3))

=max(6,5) = 6

||A-1|| = max((0.231 +0.077),(0.154 + 0.385))

=max(0.308,0.539)

=0.539

hence condition number =   ||A|| ||A-1||= 6*0.539 = 3.234

As it is small matrix is well-conditioned

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