Question 1

Solve the system, if possible.

Accepted Answer

A)  x = 8, y = -6, z = 3 
B)  x = 6, y = -7, z = 3 
C)  x = -6, y = 7, z = -3 
D)  x = 1, y = -12, z = 3 
E)  no solution; inconsistent system 
A)  x = 8, y = -6, z = 3 
B)  x = 6, y = -7, z = 3 
C)  x = -6, y = 7, z = -3 
D)  x = 1, y = -12, z = 3 
E)  no solution; inconsistent system

Question 2

Solve for x given the following equation involving a determinant.

Accepted Answer

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

Question 3

Find the inverse of the matrix.

Accepted Answer

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

Question 4

Solve the system, if possible.

Accepted Answer

A)  x = -14, y = 3, z = 4 
B)  x = -6, y = -8, z = -4 
C)  x = 6, y = 8, z = 4 
D)  x = -7, y = -6, z = 4 
E)  no solution; inconsistent system 
A)  x = -14, y = 3, z = 4 
B)  x = -6, y = -8, z = -4 
C)  x = 6, y = 8, z = 4 
D)  x = -7, y = -6, z = 4 
E)  no solution; inconsistent system

Question 5

Use a graphing calculator to find the inverse of the matrix.

Accepted Answer

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

Question 6

Find 9A.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)

Accepted Answer

A)  782 units 
B)  782 units or 852 units 
C)  852 units 
D)  831 units 
E)  no real solution 
A)  782 units 
B)  782 units or 852 units 
C)  852 units 
D)  831 units 
E)  no real solution

Question 9

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

Accepted Answer

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

Question 10

An airplane flying into a headwind travels 432 miles in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Accepted Answer

A)  plane speed = 147 mph; wind speed = 12 mph 
B)  plane speed = 109 mph; wind speed = 12 mph 
C)  plane speed = 109 mph; wind speed = 121 mph 
D)  plane speed = 147 mph; wind speed = 139 mph 
E)  plane speed = 132 mph; wind speed = 12 mph 
A)  plane speed = 147 mph; wind speed = 12 mph 
B)  plane speed = 109 mph; wind speed = 12 mph 
C)  plane speed = 109 mph; wind speed = 121 mph 
D)  plane speed = 147 mph; wind speed = 139 mph 
E)  plane speed = 132 mph; wind speed = 12 mph

Question 11

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(20, 0), R(20, 6)

Accepted Answer

A)  A = 120 
B)  A = 20 
C)  A = 60 
D)  A = 6 
E)  none of these 
A)  A = 120 
B)  A = 20 
C)  A = 60 
D)  A = 6 
E)  none of these

Question 12

Find A - B.

Accepted Answer

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

Question 13

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Accepted Answer

A)  row-echelon form 
B)  row-echelon form and reduced row-echelon form 
C)  neither 
A)  row-echelon form 
B)  row-echelon form and reduced row-echelon form 
C)  neither

Question 14

Write the augmented matrix for the system of linear equations.

Accepted Answer

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

Question 15

Solve the system by the method of elimination.

Accepted Answer

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

Question 16

Determine which one of the ordered triples below is a solution of the given system of equations.

Accepted Answer

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

Question 17

Solve the system by substitution, if possible.

Accepted Answer

A)  (9, 4) 
B)  (-4, -8) 
C)  (-4, 13) 
D)  (12, -3) 
E)  no solution; inconsistent system 
A)  (9, 4) 
B)  (-4, -8) 
C)  (-4, 13) 
D)  (12, -3) 
E)  no solution; inconsistent system

Question 18

Evaluate the expression.

Accepted Answer

A)    
B)    
C)    
D)    
E)  not possible 
A)    
B)    
C)    
D)    
E)  not possible

Question 19

If possible, find AB.

Accepted Answer

A)    
B)    
C)  not possible 
D)    
E)    
A)    
B)    
C)  not possible 
D)    
E)

Question 20

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

Accepted Answer

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

Solve the system, if possible.

Solve for x given the following equation involving a determinant.

Find the inverse of the matrix.

Solve the system, if possible.

Use a graphing calculator to find the inverse of the matrix.

Find 9A.

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

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)

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

An airplane flying into a headwind travels 432 miles in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(20, 0), R(20, 6)

Find A - B.

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Write the augmented matrix for the system of linear equations.

Solve the system by the method of elimination.

Determine which one of the ordered triples below is a solution of the given system of equations.

Solve the system by substitution, if possible.

Evaluate the expression.

If possible, find AB.

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

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

Filters

Exam 8: Linear Systems and Matrices

Solve the system, if possible.

Solve for x given the following equation involving a determinant.

Find the inverse of the matrix.

Solve the system, if possible.

Use a graphing calculator to find the inverse of the matrix.

Find 9A.

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

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)

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

An airplane flying into a headwind travels 432 miles in 3 hours and 36 minutes. On the return flight, the distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(20, 0), R(20, 6)

Find A - B.

Determine whether the matrix is in row-echelon form. If it is, determine if it is also in reduced row-echelon form.

Write the augmented matrix for the system of linear equations.

Solve the system by the method of elimination.

Determine which one of the ordered triples below is a solution of the given system of equations.

Solve the system by substitution, if possible.

Evaluate the expression.

If possible, find AB.

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

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

Filters

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

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

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