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)
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)
