Question 1

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Accepted Answer

A)    
B)     
C)     
D)    
E)     
A)    
B)     
C)     
D)    
E)     A

Question 2

Solve the system of linear equations.

Accepted Answer

A)     
B)    
C)     
D)     
E)    
A)     
B)    
C)     
D)     
E)    B

Question 3

Find the solution set of the system of linear equations in the variables x and y (in that order) that has the following augmented matrix.

Accepted Answer

A)     
B)     
C)     
D)    
E)     
A)     
B)     
C)     
D)    
E)     B

Question 4

Solve the system of linear equations.

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 5

Find the equation of the parabola   that passes through the points   .

Accepted Answer

A)     
B)     
C)     
D)    
E)    
A)     
B)     
C)     
D)    
E)

Question 6

Use back-substitution to solve the system of linear equations.

Accepted Answer

A)    
B)     
C)     
D)     
E)    
A)    
B)     
C)     
D)     
E)

Question 7

Irrigation. An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B, C, D, and E with the amounts shown. Using the fact that at each point the water entering equals the water leaving, formulate an equation for water flow at each of the five points and solve the system.

Accepted Answer

A)    ,   ,   ,   ,   (in thousands of gallons) 
B)    ,   ,   ,   ,   (in thousands of gallons) 
C)    ,   ,   ,   ,   (in thousands of gallons) 
D)    ,   ,   ,   ,   (in thousands of gallons) 
E)     ,   ,   ,   ,   (in thousands of gallons) 
A)    ,   ,   ,   ,   (in thousands of gallons) 
B)    ,   ,   ,   ,   (in thousands of gallons) 
C)    ,   ,   ,   ,   (in thousands of gallons) 
D)    ,   ,   ,   ,   (in thousands of gallons) 
E)     ,   ,   ,   ,   (in thousands of gallons)

Question 8

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Find a cubic polynomial   that fits these data

Accepted Answer

A)    
B)     
C)    
D)    
E)    
A)    
B)     
C)    
D)    
E)

Question 9

Use Gaussian elimination method to solve the system of linear equations.

Accepted Answer

A)     
B)     
C)     
D)     
E)  inconsistent system 
A)     
B)     
C)     
D)     
E)  inconsistent system

Question 10

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system

Accepted Answer

A)     amperes;   amperes;   amperes 
B)     amperes;   amperes;   amperes 
C)     amperes;   amperes;   amperes 
D)     amperes;   amperes;   amperes 
E)     amperes;   amperes;   amperes 
A)     amperes;   amperes;   amperes 
B)     amperes;   amperes;   amperes 
C)     amperes;   amperes;   amperes 
D)     amperes;   amperes;   amperes 
E)     amperes;   amperes;   amperes

Question 11

Solve the following system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. If there is no solution, state that the system is inconsistent.

Accepted Answer

A)     
B)     
C)     
D)  inconsistent system 
E)     
A)     
B)     
C)     
D)  inconsistent system 
E)

Question 12

Traffic flow. In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x1 represents the number of cars traveling between intersections A and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain
  
Formulate equations for the traffic at B, C, and D. Solve the system of these four equations.

Accepted Answer

A)    ,   ,   ,   
B)    ,   ,   ,   
C)    ,   ,   ,   
D)    ,   ,   ,   
E)     ,   ,   ,   
A)    ,   ,   ,   
B)    ,   ,   ,   
C)    ,   ,   ,   
D)    ,   ,   ,   
E)     ,   ,   ,

Question 13

The given matrix is an augmented matrix representing a system of linear equations. Find the solution of the system.

Accepted Answer

A)     
B)     
C)     
D)    
E)     
A)     
B)     
C)     
D)    
E)

Question 14

Solve the system of linear equations.

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 15

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Estimate the population in 1970 by using a cubic polynomial that fits these data.

Accepted Answer

A)  448 million 
B)  278 million 
C)  236 million 
D)  298 million 
E)  210 million 
A)  448 million 
B)  278 million 
C)  236 million 
D)  298 million 
E)  210 million

Question 16

Solve the system of equations by using graphical methods.

Accepted Answer

A)     
B)     
C)     
D)     
E)  There is no solution to the equations. 
A)     
B)     
C)     
D)     
E)  There is no solution to the equations.

Question 17

Solve the system of equations by using graphical methods.

Accepted Answer

A)    
B)    
C)     
D)     
E)  There are infinitely many solutions. 
A)    
B)    
C)     
D)     
E)  There are infinitely many solutions.

Question 18

Solve using any method.

Accepted Answer

A)     
B)     
C)    
D)   , where a is any real number 
E)  inconsistent 
A)     
B)     
C)    
D)   , where a is any real number 
E)  inconsistent

Question 19

Suppose that the net profit (in millions of dollars) for Microsoft from 2000 to 2007 is shown in the table below.     
A cubic model that matches the data for the years 2001, 2003, 2005, and 2007 is to be determined where x represents the number of years since 2000. Set up a system of equations to solve for the coefficients a0, a1, a2 and a3.

Accepted Answer

A)    
B)    
C)     
D)    
E)     
A)    
B)    
C)     
D)    
E)

Question 20

Use a system of equations to write the partial fraction decomposition of the rational expression   . 
Then solve the system using matrices.

Accepted Answer

A)     
B)     
C)    
D)    
E)     
A)     
B)     
C)    
D)    
E)

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Solve the system of linear equations.

Find the solution set of the system of linear equations in the variables x and y (in that order) that has the following augmented matrix.

Solve the system of linear equations.

Find the equation of the parabola that passes through the points .

Use back-substitution to solve the system of linear equations.

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Find a cubic polynomial that fits these data

Use Gaussian elimination method to solve the system of linear equations.

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system

Solve the following system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. If there is no solution, state that the system is inconsistent.

The given matrix is an augmented matrix representing a system of linear equations. Find the solution of the system.

Solve the system of linear equations.

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Estimate the population in 1970 by using a cubic polynomial that fits these data.

Solve the system of equations by using graphical methods.

Solve the system of equations by using graphical methods.

Solve using any method.

Use a system of equations to write the partial fraction decomposition of the rational expression $Use a system of equations to write the partial fraction decomposition of the rational expression . Then solve the system using matrices.$ . Then solve the system using matrices.

Matrices

Determinants

Vector Spaces

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Exam 1: Linear Equations

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.)

Solve the system of linear equations.

Find the solution set of the system of linear equations in the variables x and y (in that order) that has the following augmented matrix.

Solve the system of linear equations.

Find the equation of the parabola that passes through the points .

Use back-substitution to solve the system of linear equations.

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Find a cubic polynomial that fits these data

Use Gaussian elimination method to solve the system of linear equations.

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I1, I2, and I3 are the solution of the system

Solve the following system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. If there is no solution, state that the system is inconsistent.

The given matrix is an augmented matrix representing a system of linear equations. Find the solution of the system.

Solve the system of linear equations.

Suppose that the U. S. population for the years 1920, 1930, 1940, and 1950 is shown in the table below. Let x represent the number of decades since 1920. Estimate the population in 1970 by using a cubic polynomial that fits these data.

Solve the system of equations by using graphical methods.

Solve the system of equations by using graphical methods.

Solve using any method.

Use a system of equations to write the partial fraction decomposition of the rational expression . Then solve the system using matrices.

Matrices

Determinants

Vector Spaces

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system

Use a system of equations to write the partial fraction decomposition of the rational expression $Use a system of equations to write the partial fraction decomposition of the rational expression . Then solve the system using matrices.$ . Then solve the system using matrices.