Deck 8: Linear Systems and Matrices

Question 1

Solve using any method.

A)
B)
C)
D)
E) inconsistent

Answer 1

Question 2

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.)

A) 254 units
B) 254 units or 281 units
C) 272 units
D) 281 units
E) no real solution

Answer 2

281 units

Question 3

Evaluate the expression.

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

Answer 3

Question 4

If possible, find AB.

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

Question 5

Evaluate the expression.

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

Question 6

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.

A)

B)

C)

D)

E)

Question 7

Solve the system by the method of elimination.

A)
B) inconsistent
C)
D)
E)

Question 8

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 239 tickets and collected $1389. If adult tickets sold for $10 and children's tickets sold for $3, how many of each type of ticket were sold?

A) adult tickets sold = 92; children's tickets sold = 156
B) adult tickets sold = 143; children's tickets sold = 96
C) adult tickets sold = 139; children's tickets sold = 92
D) adult tickets sold = 92; children's tickets sold = 139
E) adult tickets sold = 96; children's tickets sold = 143

Question 9

Solve using any method.

A)
B) inconsistent
C)
D)
E)

Question 10

Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply

A)
B)
C)
D) inconsistent
E)

Question 11

Solve the system by the method of substitution.

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

Question 12

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.

A) I₁ = 3, I₂ = 3, I₃ = 6
B) I₁ = 4, I₂ = 2, I₃ = 6
C) I₁ = 4, I₂ = 6, I₃ = 2
D) I₁ = 3, I₂ = 3, I₃ = 7
E) no solution

Question 13

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

A)
B)
C)
D)
E)

Question 14

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

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

Question 15

If possible, find 3A - 2B.

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

Question 16

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

A) x = -4, y = -2, z = 5
B) x = -2, y = 4, z = -5
C) no solution
D) x = -4, y = 2, z = 5
E) x = 4, y = 2, z = 5

Question 17

Write the augmented matrix for the system of linear equations.

A)
B)
C)
D)
E)

Question 18

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.

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 19

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

A)
B)
C)
D)
E)

Question 20

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

A)
B)
C)
D)
E)

Question 21

Write the augmented matrix for the system of linear equations.

A)
B)
C)
D)
E)

Question 22

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 218 tickets and collected $1410. If adult tickets sold for $7 and children's tickets sold for $6, how many of each type of ticket were sold?

A) adult tickets sold = 80; children's tickets sold = 141
B) adult tickets sold = 94; children's tickets sold = 80
C) adult tickets sold = 102; children's tickets sold = 116
D) adult tickets sold = 116; children's tickets sold = 102
E) adult tickets sold = 80; children's tickets sold = 94

Question 23

Solve the system by the method of elimination.

A) inconsistent
B)
C)
D)
E)

Question 24

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

A) x = 5, y = -2, z = -6
B) x = 2, y = -5, z = 6
C) x = -2, y = -5, z = 6
D) no solution
E) x = 2, y = 5, z = 6

Question 25

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

A)
B)
C)
D)
E)

Question 26

Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply

A)
B) inconsistent
C)
D)
E)

Question 27

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 = 284 feet
At t = 2 seconds, s = 221 feet
At t = 3 seconds, s = 126 feet

A)
B)
C)
D)
E)

Question 28

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.

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 29

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

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

Question 30

Find the determinant of .

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

Question 31

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

A)
B)
C)
D)
E)

Question 32

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.

A)

B)

C)

D)

E)

Question 33

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

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

Question 34

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

A)
B)
C)
D)
E)

Question 35

Solve the system by the method of substitution.

A) (-4, 2)
B) (2, -4)
C) (-2, -4)
D) (-4, -2)
E) (4, 2)

Question 36

Solve for x given the following equation involving a determinant.

A)
B)
C)
D)
E)

Question 37

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.)

A) 904 units
B) 837 units
C) 837 units or 904 units
D) no real solution
E) 882 units

Question 38

Solve using any method.

A)
B)
C)
D)
E) inconsistent

Question 39

Solve using any method.

A)
B)
C)
D) inconsistent
E)

Question 40

Find the determinant of the matrix .

A)
B)
C)
D)
E)

Question 41

Solve the system by the method of elimination.

A)
B)
C)
D)
E) inconsistent

Question 42

Solve for x given the following equation involving a determinant.

A)
B)
C)
D)
E)

Question 43

Evaluate the expression.

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

Question 44

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

A)
B)
C)
D)
E)

Question 45

Find the determinant of .

A) -828
B) 512
C) -768
D) -736
E) -64

Question 46

Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.) Demand
Supply

A)
B)
C)
D)
E) inconsistent

Question 47

Solve using any method.

A)
B)
C)
D)
E) inconsistent

Question 48

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

A)
B)
C)
D)
E)

Question 49

Solve using any method.

A)
B)
C)
D)
E) inconsistent

Question 50

If possible, find 5A - 4B.

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

Question 51

Find the determinant of the matrix .

A)
B)
C)
D)
E)

Question 52

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

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

Question 53

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

A) adult tickets sold = 97; children's tickets sold = 125
B) adult tickets sold = 86; children's tickets sold = 114
C) adult tickets sold = 114; children's tickets sold = 86
D) adult tickets sold = 125; children's tickets sold = 97
E) adult tickets sold = 97; children's tickets sold = 99

Question 54

If possible, find AB.

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

Question 55

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.

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

Question 56

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.)

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

Question 57

An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A) plane speed = 109 mph; wind speed = 101 mph
B) plane speed = 109 mph; wind speed = 14 mph
C) plane speed = 71 mph; wind speed = 83 mph
D) plane speed = 71 mph; wind speed = 14 mph
E) plane speed = 94 mph; wind speed = 14 mph

Question 58

Evaluate the expression.

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

Question 59

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 = 161 feet
At t = 2 seconds, s = 98 feet
At t = 3 seconds, s = 3 feet

A)
B)
C)
D)
E)

Question 60

Solve the system by the method of substitution.

A) (4, 3)
B) (-3, 4)
C) (3, 4)
D) (4, -3)
E) (-4, 3)

Question 61

Solve the system of equations by graphing.

A) (-4, 6)
B) (-5, 5)
C) (6, 1)
D) (5, -5)
E) (3, 13)

Question 62

Find the determinant of the matrix .

A)
B)
C)
D)
E)

Question 63

Evaluate the expression.

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

Question 64

If possible, find AB.

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

Question 65

Evaluate the expression.

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

Question 66

Solve the system.

A)
B)
C)
D)
E) no solution

Question 67

If possible, find 2A - 5B.

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

Question 68

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

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

Question 69

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

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

Question 70

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.

A)

B)

C)

D)

E)

Question 71

Solve for x given the following equation involving a determinant.

A)
B)
C)
D)
E)

Question 72

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

A)
B)
C)
D)
E)

Question 73

Use matrices to solve the system of equations (if possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.

A) x = -5, y = -3, z = 2
B) x = 5, y = -3, z = 2
C) x = 5, y = 3, z = 2
D) x = 3, y = -5, z = -2
E) no solution

Question 74

Find the determinant of .

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

Question 75

Write the augmented matrix for the system of linear equations.

A)
B)
C)
D)
E)

Question 76

Determine which ordered pair is a solution of the system.

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

Question 77

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.

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 78

Solve the system by substitution, if possible.

A) (4, 8)
B) (8, 4)
C) (-4, 13)
D) (12, -3)
E) no solutions

Question 79

Determine which ordered pair is a solution of the system.

A) (8, 1)
B) (-9, 3)
C) (-9,8)
D) (8, -1)
E) (1, -8)

Question 80

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

A)
B)
C)
D)
E)