Question 1

Find the product.

Accepted Answer

A)    
B)    
C)    
D)  cannot multiply 
E)    
A)    
B)    
C)    
D)  cannot multiply 
E)

Question 2

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

Accepted Answer

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

Question 3

An airplane flying into a headwind travels 690 miles in 3 hours and 50 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 = 220 mph; wind speed = 25 mph 
B)  plane speed = 182 mph; wind speed = 194 mph 
C)  plane speed = 205 mph; wind speed = 25 mph 
D)  plane speed = 220 mph; wind speed = 212 mph 
E)  plane speed = 182 mph; wind speed = 25 mph 
A)  plane speed = 220 mph; wind speed = 25 mph 
B)  plane speed = 182 mph; wind speed = 194 mph 
C)  plane speed = 205 mph; wind speed = 25 mph 
D)  plane speed = 220 mph; wind speed = 212 mph 
E)  plane speed = 182 mph; wind speed = 25 mph

Question 4

Find the determinant of   .

Accepted Answer

A)  14 
B)  7 
C)  12 
D)  -8 
E)  6 
A)  14 
B)  7 
C)  12 
D)  -8 
E)  6

Question 5

Find A - B.

Accepted Answer

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

Question 6

The currents in an electrical network are given by the solutions of the system   where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

Accepted Answer

A)  I1 = 5, I2 = 8, I3 = 3 
B)  I1 = 5, I2 = 3, I3 = 8 
C)  I1 = 3, I2 = 5, I3 = 9 
D)  I1 = 3, I2 = 5, I3 = 8 
E)  no solution 
A)  I1 = 5, I2 = 8, I3 = 3 
B)  I1 = 5, I2 = 3, I3 = 8 
C)  I1 = 3, I2 = 5, I3 = 9 
D)  I1 = 3, I2 = 5, I3 = 8 
E)  no solution

Question 7

An object moving vertically is at the given heights at the specified times. Find the position equation   for the object. At t = 1 second, s = 421 feet
At t = 2 seconds, s = 358 feet
At t = 3 seconds, s = 263 feet

Accepted Answer

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

Question 8

Use Cramer's rule to find the solution of the system, if possible.

Accepted Answer

A)  x = 2, y = -2 
B)  x = 7, y = -16 
C)  x = 7, y = -7 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  x = 2, y = -2 
B)  x = 7, y = -16 
C)  x = 7, y = -7 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 9

Determine which ordered pair is a solution of the system.

Accepted Answer

A)  (-3, 6) 
B)  (-1, -2) 
C)  (-2, -1) 
D)  (1, -2) 
E)  (6, 3) 
A)  (-3, 6) 
B)  (-1, -2) 
C)  (-2, -1) 
D)  (1, -2) 
E)  (6, 3)

Question 10

Use Cramer's Rule to solve the following system of linear equations:

Accepted Answer

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

Question 11

Solve the system using Gauss-Jordan elimination.

Accepted Answer

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

Question 12

Find the product.

Accepted Answer

A)    
B)    
C)    
D)  102 
E)    
A)    
B)    
C)    
D)  102 
E)

Question 13

Solve the system by Gauss - Jordan elimination.

Accepted Answer

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

Question 14

Determine which ordered pair is a solution of the system.

Accepted Answer

A)  (6, -4) 
B)  (-7, 1) 
C)  (-7,-3) 
D)  (-4, -6) 
E)  (6, 4) 
A)  (6, -4) 
B)  (-7, 1) 
C)  (-7,-3) 
D)  (-4, -6) 
E)  (6, 4)

Question 15

Find the inverse of the matrix   (if it exists).

Accepted Answer

A)    
B)    
C)  does not exist 
D)    
E)    
A)    
B)    
C)  does not exist 
D)    
E)

Question 16

Solve the system by Gauss - Jordan elimination.

Accepted Answer

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

Question 17

Solve the system, if possible.

Accepted Answer

A)  x = -6, y = -9, z = -3 
B)  x = -8, y = 2, z = 3 
C)  x = 3, y = -8, z = -3 
D)  x = 8, y = -2, z = -3 
E)  no solution; inconsistent system 
A)  x = -6, y = -9, z = -3 
B)  x = -8, y = 2, z = 3 
C)  x = 3, y = -8, z = -3 
D)  x = 8, y = -2, z = -3 
E)  no solution; inconsistent system

Question 18

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

Accepted Answer

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

Question 19

Solve using any method.

Accepted Answer

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

Question 20

The currents in an electrical network are given by the solutions of the system   where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

Accepted Answer

A)  I1 = 4, I2 = 5, I3 = 9 
B)  I1 = 2, I2 = 3, I3 = 6 
C)  I1 = 2, I2 = 3, I3 = 5 
D)  I1 = 4, I2 = 9, I3 = 5 
E)  no solution 
A)  I1 = 4, I2 = 5, I3 = 9 
B)  I1 = 2, I2 = 3, I3 = 6 
C)  I1 = 2, I2 = 3, I3 = 5 
D)  I1 = 4, I2 = 9, I3 = 5 
E)  no solution

Find the product.

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

An airplane flying into a headwind travels 690 miles in 3 hours and 50 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.

Find the determinant of .

Find A - B.

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.

An object moving vertically is at the given heights at the specified times. Find the position equation for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet

Use Cramer's rule to find the solution of the system, if possible.

Determine which ordered pair is a solution of the system.

Use Cramer's Rule to solve the following system of linear equations:

Solve the system using Gauss-Jordan elimination.

Find the product.

Solve the system by Gauss - Jordan elimination.

Determine which ordered pair is a solution of the system.

Find the inverse of the matrix (if it exists).

Solve the system by Gauss - Jordan elimination.

Solve the system, if possible.

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

Solve using any method.

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.

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

Find the product.

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

An airplane flying into a headwind travels 690 miles in 3 hours and 50 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.

Find the determinant of .

Find A - B.

The currents in an electrical network are given by the solutions of the system where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

An object moving vertically is at the given heights at the specified times. Find the position equation for the object. At t = 1 second, s = 421 feet At t = 2 seconds, s = 358 feet At t = 3 seconds, s = 263 feet

Use Cramer's rule to find the solution of the system, if possible.

Determine which ordered pair is a solution of the system.

Use Cramer's Rule to solve the following system of linear equations:

Solve the system using Gauss-Jordan elimination.

Find the product.

Solve the system by Gauss - Jordan elimination.

Determine which ordered pair is a solution of the system.

Find the inverse of the matrix (if it exists).

Solve the system by Gauss - Jordan elimination.

Solve the system, if possible.

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

Solve using any method.

The currents in an electrical network are given by the solutions of the system where I1, I2, and I3 are measured in amperes. Solve the system of equations using matrices.

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

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.

The currents in an electrical network are given by the solutions of the system where I₁, I₂, and I₃ are measured in amperes. Solve the system of equations using matrices.