Question 1

If possible, find AB.

Accepted Answer

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

Question 2

Write the augmented matrix for the system of linear equations.

Accepted Answer

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

Question 3

Solve the system using Gauss-Jordan elimination.

Accepted Answer

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

Question 4

Solve the system, if possible.

Accepted Answer

A)  x = -6, y = 1, z = -3 
B)  x = 6, y = -1, z = 3 
C)  x = 5, y = 8, z = -3 
D)  x = 0, y = 6, z = -3 
E)  no solution; inconsistent system 
A)  x = -6, y = 1, z = -3 
B)  x = 6, y = -1, z = 3 
C)  x = 5, y = 8, z = -3 
D)  x = 0, y = 6, z = -3 
E)  no solution; inconsistent system

Question 5

Solve the system by substitution, if possible.

Accepted Answer

A)  (5, 2) 
B)  (3, 2) 
C)  (2, 5) 
D)  (1, 6) 
E)  no solutions 
A)  (5, 2) 
B)  (3, 2) 
C)  (2, 5) 
D)  (1, 6) 
E)  no solutions

Question 6

Solve the system by substitution, if possible.

Accepted Answer

A)  (2, 7) 
B)  (-5, 10) 
C)  (9, -4) 
D)  (7, 2) 
E)  no solutions 
A)  (2, 7) 
B)  (-5, 10) 
C)  (9, -4) 
D)  (7, 2) 
E)  no solutions

Question 7

Solve the system by the method of elimination.

Accepted Answer

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

Question 8

Solve using any method.

Accepted Answer

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

Question 9

Evaluate the expression.

Accepted Answer

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

Question 10

Find the determinant of   .

Accepted Answer

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

Question 11

Find the product.

Accepted Answer

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

Question 12

Find the inverse of the matrix.

Accepted Answer

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

Question 13

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 = 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 
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 14

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

Accepted Answer

A)  x = 1, y = -1 
B)  x = 7, y = -8 
C)  x = 7, y = -7 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  x = 1, y = -1 
B)  x = 7, y = -8 
C)  x = 7, y = -7 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 15

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 = -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 
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 16

If possible, find AB.

Accepted Answer

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

Question 17

Find the determinant of the matrix   .

Accepted Answer

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

Question 18

Solve the system.

Accepted Answer

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

Question 19

Solve the system by the method of substitution.

Accepted Answer

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

Question 20

Solve the system by substitution, if possible.

Accepted Answer

A)  (-4, 11) 
B)  (10, -3) 
C)  (-3, 10) 
D)  (3, 7) 
E)  no solutions 
A)  (-4, 11) 
B)  (10, -3) 
C)  (-3, 10) 
D)  (3, 7) 
E)  no solutions

If possible, find AB.

Write the augmented matrix for the system of linear equations.

Solve the system using Gauss-Jordan elimination.

Solve the system, if possible.

Solve the system by substitution, if possible.

Solve the system by substitution, if possible.

Solve the system by the method of elimination.

Solve using any method.

Evaluate the expression.

Find the determinant of .

Find the product.

Find the inverse of the matrix.

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.

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

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

If possible, find AB.

Find the determinant of the matrix .

Solve the system.

Solve the system by the method of substitution.

Solve the system by substitution, if possible.

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

If possible, find AB.

Write the augmented matrix for the system of linear equations.

Solve the system using Gauss-Jordan elimination.

Solve the system, if possible.

Solve the system by substitution, if possible.

Solve the system by substitution, if possible.

Solve the system by the method of elimination.

Solve using any method.

Evaluate the expression.

Find the determinant of .

Find the product.

Find the inverse of the matrix.

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.

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

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

If possible, find AB.

Find the determinant of the matrix .

Solve the system.

Solve the system by the method of substitution.

Solve the system by substitution, if possible.

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.