NUMERICAL METHODS EXAM 2 CONVERGENCE OPTIMIZER TOOLKIT: HIGHYIELD SOLVED QUESTIONS AND FINAL EVALUATION TRANSCRIPT FOR ALGORITHMIC SUCCESS 2026

NUMERICAL METHODS EXAM 2
CONVERGENCE OPTIMIZER TOOLKIT: HIGH-
YIELD SOLVED QUESTIONS AND FINAL
EVALUATION TRANSCRIPT FOR
ALGORITHMIC SUCCESS 2026

◍ A system is consistent if it has at least one solution(T/F). Answer:
True


◍ Integration is equivalent to finding the area under a function for
positive functions.. Answer: True


◍ The determinant of a matrix is the same as the determinant of the
transpose of the matrix.. Answer: True


◍ Gauss Elimination is the systematic process of removing
unknowns using forward elimination followed by back substitution to
obtain the unknown values.. Answer: True


◍ eye(3) will generate a 3x3 identity matrix. (T/F). Answer: True


◍ The Composite Simpson's 3/8 Rule can be used to obtain the
integral over an interval divided into n=5 segments.. Answer: False

, ◍ The key to Gauss Quadrature is to balance the function values at
the endpoints.. Answer: True


◍ The Hybrid Simpson's approach can be used to obtain the integral
over an interval divided into n=5 segments.. Answer: True


◍ The method of undetermined coefficients is an approach to finding
the particular solution to certain nonhomogenous ordinary differential
equations.. Answer: True


◍ For small step size h, decreasing the step size by half will result in
less error than using a more accurate version (e.g. using an O(h2)
method instead of an O(h) method).. Answer: False


◍ If one row of a matrix is a linear combination of two other rows,
then the determinant is zero.. Answer: True


◍ The determinant of ill-conditions systems is zero or nearly zero..
Answer: True


◍ If the error of an integration technique is proportional to h^2, we
say the error is of order h^2, which we write as O(h^2).. Answer: True


◍ Simpson's 1/3 Rule can be used to calculate the integral of a
function or data with unequal-width segments.. Answer: False