CE 2020 Exam #3 Review Questions and answers, rated A+/ 2024/25 Exam PREDICTOR PAPER

CE 2020 Exam #3 Review Questions and answers, rated A+ Briefly explain what the graphical method for solving a system of two algebraic linear equations is. Provide a diagram representing the two equations Plot the two equations with cartesian coordinates and axis labeled x1 and x2. Equations have variables of x1 and x2 (will plot straight lines. Should draw 3 graphs, 1 with no solution, one with infinite solutions, one that is ill-conditioned) In the context of solving a system of linear algebraic equations, what does the system ill-conditioned systemmeans? Where the slopes of two equations are so close that it is hard to pinpoint the exact solution -What does the MATLAB built det() function in function det() do? What is the argument for the function? Finds the determinant of a matrix You should know that the determinant of the matrix of coefficients for a linear system of equations will be _______ if the system has no solution. Zero You should know that the determinant of the matrix of coefficients for a linear system of equations will be _____ if the system has an infinite number of solutions (i.e., it is singular). Zero -You should know that the determinant of the matrix of coefficients for a linear system of equations will be _________ if the system is ill conditioned. Close to zero You should know that the Cramer's rule for solving a system of linear equations is useful (and so it is of practical significance) only when the number of equations in the system is small (e.g., when the system is formed by two or three equations, and therefore there are two or three unknowns). Cramer's rule is useful as long as matrix is 2x2 or 3x3 but has difficulty with large systems You should know that the Cramer's rule for solving a system of linear equations computes the different unknowns by evaluating a ratio of two determinants. The denominator in this ratio is the determinant of the matrix of coefficients. The numerator in this ratio is the determinant of the matrix of coefficients with the column of coefficients corresponding to the unknown replaced by the coefficients in the vector of constants. You are expected to know how to apply Cramer's rule if given a simple problem involving, for example, a system of two linear equations with two unknowns. (Sent in drawing) You are expected to know what the method of Elimination of Unknowns for solving a system of algebraic linear equations is. You are also expected to be able to illustrate the application of the method (applying the correct/formal procedure for eliminating unknowns as done in the textbook) if given a small system of linear equations (e.g., a system consisting of two equations and two unknowns). Multiply the equations by constants so that one of the unknowns will be eliminated when the equations are combined(illustration sent in text) The Naive Gauss Elimination method for solving systems of linear algebraic equations (of any size) is a generalization of the method of elimination of unknowns (which is typically used to solve systems of small number of equations). Which are the two main steps needed to apply the Naive Gauss Elimination method? Why is the method called 'Naive'? 1. Equations were manipulated to eliminate one of the unknowns from the equations (elimination) 2. Equations should be solved directly and then back substituted into one of the original equations to find the remaining unknown. Method is called Naive because it does NOT avoid division by zero. In the context of solving a system of linear algebraic equations, explain what pivoting is. Explain the difference between partial pivoting and complete pivoting. Multiplying all elements in a system of an