Question 1

Solve the system, if possible.

Accepted Answer

A)  x = -8, y = 4, z = 2 
B)  x = 8, y = -4, z = -2 
C)  x = -4, y = -11, z = -2 
D)  x = 5, y = -8, z = -2 
E)  no solution; inconsistent system 
A)  x = -8, y = 4, z = 2 
B)  x = 8, y = -4, z = -2 
C)  x = -4, y = -11, z = -2 
D)  x = 5, y = -8, z = -2 
E)  no solution; inconsistent system

Question 2

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(12, 0), R(12, 9)

Accepted Answer

A)  A = 54 
B)  A = 9 
C)  A = 12 
D)  A = 108 
E)  none of these 
A)  A = 54 
B)  A = 9 
C)  A = 12 
D)  A = 108 
E)  none of these

Question 3

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 4

Evaluate the expression.

Accepted Answer

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

Question 5

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.

Accepted Answer

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 
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 6

Determine which ordered pair is a solution of the system.

Accepted Answer

A)  (1, -2) 
B)  (-3, 9) 
C)  (2, -1) 
D)  (2, 1) 
E)  (-3,-9) 
A)  (1, -2) 
B)  (-3, 9) 
C)  (2, -1) 
D)  (2, 1) 
E)  (-3,-9)

Question 7

Evaluate the expression.

Accepted Answer

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

Question 8

Find the product.

Accepted Answer

A)    
B)    
C)    
D)    
E)  99 
A)    
B)    
C)    
D)    
E)  99

Question 9

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

Accepted Answer

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

Question 10

Find A - B.

Accepted Answer

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

Question 11

Solve for x given the following equation involving a determinant.

Accepted Answer

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

Question 12

Solve the system using Gauss-Jordan elimination.

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

Question 14

Find the product.

Accepted Answer

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

Question 15

Find the inverse of the matrix.

Accepted Answer

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

Question 16

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Find 8A.

Accepted Answer

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

Question 20

Solve the system.

Accepted Answer

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

Solve the system, if possible.

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(12, 0), R(12, 9)

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

Evaluate the expression.

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.

Determine which ordered pair is a solution of the system.

Evaluate the expression.

Find the product.

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

Find A - B.

Solve for x given the following equation involving a determinant.

Solve the system using Gauss-Jordan elimination.

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

Find the product.

Find the inverse of the matrix.

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.)

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

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

Find 8A.

Solve the system.

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.

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(12, 0), R(12, 9)

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

Evaluate the expression.

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.

Determine which ordered pair is a solution of the system.

Evaluate the expression.

Find the product.

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

Find A - B.

Solve for x given the following equation involving a determinant.

Solve the system using Gauss-Jordan elimination.

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

Find the product.

Find the inverse of the matrix.

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.)

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

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

Find 8A.

Solve the system.

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