Question 1

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(16, 0), R(16, 5)

Accepted Answer

A)  A = 5 
B)  A = 80 
C)  A = 40 
D)  A = 16 
E)  none of these 
A)  A = 5 
B)  A = 80 
C)  A = 40 
D)  A = 16 
E)  none of these

Question 2

Solve the system by substitution, if possible.

Accepted Answer

A)  (11, 0) 
B)  (5, 6) 
C)  (0, 11) 
D)  (-1, 12) 
E)  no solutions 
A)  (11, 0) 
B)  (5, 6) 
C)  (0, 11) 
D)  (-1, 12) 
E)  no solutions

Question 3

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

Question 4

Solve the system of equations by graphing.

Accepted Answer

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

Question 5

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

Accepted Answer

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 
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 6

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 7

Solve the system using Gaussian elimination.

Accepted Answer

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

Question 8

Solve using any method.

Accepted Answer

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

Question 9

Solve the system by substitution, if possible.

Accepted Answer

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

Question 10

Solve for x given the following equation involving a determinant.

Accepted Answer

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

Question 11

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?

Accepted Answer

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 
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 12

Find the cofactor C 12 of the matrix.

Accepted Answer

A)  C 12 = -3 
B)  C 12 = 2 
C)  C 12 = -2 
D)  C 12 = 3 
E)  none of these 
A)  C 12 = -3 
B)  C 12 = 2 
C)  C 12 = -2 
D)  C 12 = 3 
E)  none of these

Question 13

Find the product.

Accepted Answer

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

Question 14

Find the inverse of the matrix.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

If possible, find 2A - 5B.

Accepted Answer

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

Question 17

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

Accepted Answer

A)  x = 6, y = -6 
B)  x = 2, y = -2 
C)  x = 6, y = -14 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  x = 6, y = -6 
B)  x = 2, y = -2 
C)  x = 6, y = -14 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 18

Find the inverse of the matrix.

Accepted Answer

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

Question 19

Solve the system, if possible.

Accepted Answer

A)  x = 9, y = -6, z = 6 
B)  x = 1, y = 8, z = -6 
C)  x = -1, y = -8, z = 6 
D)  x = 9, y = 1, z = 6 
E)  no solution; inconsistent system 
A)  x = 9, y = -6, z = 6 
B)  x = 1, y = 8, z = -6 
C)  x = -1, y = -8, z = 6 
D)  x = 9, y = 1, z = 6 
E)  no solution; inconsistent system

Question 20

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

Accepted Answer

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 
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

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(16, 0), R(16, 5)

Solve the system by substitution, if possible.

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

Solve the system of equations by graphing.

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

Solve the system using Gaussian elimination.

Solve using any method.

Solve the system by substitution, if possible.

Solve for x given the following equation involving a determinant.

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?

Find the cofactor C₁₂ of the matrix.

Find the product.

Find the inverse of the matrix.

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

If possible, find 2A - 5B.

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

Find the inverse of the matrix.

Solve the system, if possible.

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

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

Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(16, 0), R(16, 5)

Solve the system by substitution, if possible.

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

Solve the system of equations by graphing.

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

Solve the system using Gaussian elimination.

Solve using any method.

Solve the system by substitution, if possible.

Solve for x given the following equation involving a determinant.

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?

Find the cofactor C 12 of the matrix.

Find the product.

Find the inverse of the matrix.

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

If possible, find 2A - 5B.

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

Find the inverse of the matrix.

Solve the system, if possible.

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

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

Find the cofactor C₁₂ of the matrix.