MAE 284 FINAL EXAM 2026/2027 LATEST UPDATE (6pages)

All mathematical problems have closed-form solution(i.e. they can be solved for a variable having to make guesses) (T/F) - answerFalse All variables that have been defined are found in the command window, even empty ones(T/F) - answerFalse Anonymous functions need to be defined before being used(T/F) - answerTrue Given two vectors a and b, which command would you use to calculate the cross product of a and b? - answercross(a,b) The bisection algorithm is an open method(T/F) - answerFalse The bisection method is most effective when there are multiple roots inside a bracket (T/F) - answerFalse A false position method is based on the false assumption that the function can be approximated by a(n) - answerstraight line One disadvantage of the Newton-Raphson method is that it requires the user to analytically find the derivative of the function(T/F) - answerTrue For the fourth iteration in the Newton-Raphson method, you will use the estimated root location from the third iteration as the new initial point(T/F) - answerTrue Which one of the following functions can be used to find the list of the lower bound and upper bound that bracket a root? - answerincsearch Quadrature is another name for integration(T/F) - answerTrue The key to Guass Quadrature is to balance the function values(T/F) - answerFalse The trapezoidal rule approximates the function by a: - answerstraight line The Guass Quadrature formulas we discussed in class are called Guess-Legendre formulas.(T/F) - answerTrue Romberg's method is NOT a newton-Cotes method.(T/F) - answerFalse Simpsons 3/8 rule approximates the function by a _____ order polynomial - answerThird The composite Simpson's 1/3 rule requires the number of segments be: - answerEven The key to Guass Quadrature is to balance the positive and negative errors.(T/F) - answerTrue Naive Guass elimination ensures that division by zero is not possible(T/F) - answerFalse If the determinant of a matrix is zero, the inverse of the matric is a scalar.(T/F) - answerFalse If two rows of a matrix are identical, the determinant is zero.(T/F) - answerTrue If one row of a matrix consists entirely of zeros, then the determinant is zero(T/F) - answerTru