= Consider the root finding problem P(a, z) = 0 with P(a, z) = {j=0 a;z'. Let za be a solution of P(a, z) = 0 for given vector of coefficients a. Show that if we perturb a single coefficient a; by an amount of Aaj to first order the zero z is perturbed by -z' Aaj z. -(a,z) = ap z Based on this perturbation result state the condition number of a zero of P with respect to a perturbation in the coefficient a;. Note, a formal proof that your stated condition number satisfies the general definition of condition number is not required. = Consider the root finding problem P(a, z) = 0 with P(a, z) = {j=0 a;z'. Let za be a solution of P(a, z) = 0 for given vector of coefficients a. Show that if we perturb a single coefficient a; by an amount of Aaj to first order the zero z is perturbed by -z' Aaj z. -(a,z) = ap z Based on this perturbation result state the condition number of a zero of P with respect to a perturbation in the coefficient a;. Note, a formal proof that your stated condition number satisfies the general definition of condition number is not required