2. (10pt) We recall that the condition number (A) and the component wise relative condition number Ker(A) are defined, respectively, as *(A) = || A|| | ||A-'| KCR = |||A| All Consider a diagonal matrix D = diag(1,10-1.10-2..., 10-"). Evaluate x(D) and NOR(D). Evaluate the relative error of solving De = b. if D is known exactly and but b is perturbed, 6 +86. Assume that all arithmetic operations are precise (there is no rounding errors). Specifically, let i = 2 + 8x be the solution to Di = b + 86. Compute 18 le & Which condition number is predicting the relative error more accurately? 2. (10pt) We recall that the condition number (A) and the component wise relative condition number Ker(A) are defined, respectively, as *(A) = || A|| | ||A-'| KCR = |||A| All Consider a diagonal matrix D = diag(1,10-1.10-2..., 10-"). Evaluate x(D) and NOR(D). Evaluate the relative error of solving De = b. if D is known exactly and but b is perturbed, 6 +86. Assume that all arithmetic operations are precise (there is no rounding errors). Specifically, let i = 2 + 8x be the solution to Di = b + 86. Compute 18 le & Which condition number is predicting the relative error more accurately