Question 1

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

Accepted Answer

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

Question 2

Evaluate the determinant of the matrix below.

Accepted Answer

A)  3 
B)  -2 
C)  5 
D)  24 
E)  32 
A)  3 
B)  -2 
C)  5 
D)  24 
E)  32

Question 3

Consider the circuit shown in the figure below.The currents   ( in amperes ) are the solutions to the system of linear equations   , where   are voltages of 9 and 9 volts, respectively.Use the inverse of the coefficient matrix of this system to find the unknown currents.Round answers to nearest tenth.[Hint: If a current value turns out to be negative, it simply means that the current flow is in the opposite direction from that indicated in the figure below.]

Accepted Answer

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

Question 4

Find A2.(Note: A2 = AA.)

Accepted Answer

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

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)  (19a + 105, -3a - 17, a) where a is any real number 
B)  (-9a - 11, -7a - 35, a) where a is any real number 
C)  (-12a + 96, -12a + 37, a) where a is any real number 
D)  (-125a + 105, 6a - 17, a) where a is any real number 
E)  (-17a - 33, 6a - 17, a) where a is any real number 
A)  (19a + 105, -3a - 17, a) where a is any real number 
B)  (-9a - 11, -7a - 35, a) where a is any real number 
C)  (-12a + 96, -12a + 37, a) where a is any real number 
D)  (-125a + 105, 6a - 17, a) where a is any real number 
E)  (-17a - 33, 6a - 17, a) where a is any real number

Question 6

Use the matrix capabilities of a graphing utility to evaluate the expression.

Accepted Answer

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

Question 7

Given   , find

Accepted Answer

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

Question 8

Write a cryptogram for the message "TWO IF BY LAND" using the matrix   Show all your work.

Accepted Answer

The answer of Write a cryptogram for the message "TWO...

Question 9

A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility.Some of the money was borrowed at 9%, some at 11%, and some at 14%.Use a system of equations to determine how much was borrowed at 9% if the total annual interest was $216,000 and the amount borrowed at 9% was twice the amount borrowed at 14%.Solve the system using matrices.

Accepted Answer

A)  $400,000 was borrowed at 9% 
B)  $800,000 was borrowed at 9% 
C)  $300,000 was borrowed at 9% 
D)  $1,600,000 was borrowed at 9% 
E)  $1,700,000 was borrowed at 9% 
A)  $400,000 was borrowed at 9% 
B)  $800,000 was borrowed at 9% 
C)  $300,000 was borrowed at 9% 
D)  $1,600,000 was borrowed at 9% 
E)  $1,700,000 was borrowed at 9%

Question 10

Write the augmented matrix of the system of equations below.

Accepted Answer

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

Question 11

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

Accepted Answer

A)  x = -2, y = 1 
B)  x = 2, y = -1 
C)  x = -1, y = 2 
D)  x = -1, y = -2 
E)  no solution 
A)  x = -2, y = 1 
B)  x = 2, y = -1 
C)  x = -1, y = 2 
D)  x = -1, y = -2 
E)  no solution

Question 12

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

Accepted Answer

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

Question 13

If possible, find AB.

Accepted Answer

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

Question 14

Given   , use   to decode the following cryptogram:

Accepted Answer

A)  MATHEMATICIAN GALOIS 
B)  MATHEMATICIAN JACOBI 
C)  MATHEMATICIAN EUCLID 
D)  MATHEMATICIAN PASCAL 
E)  MATHEMATICIAN AGNESI 
A)  MATHEMATICIAN GALOIS 
B)  MATHEMATICIAN JACOBI 
C)  MATHEMATICIAN EUCLID 
D)  MATHEMATICIAN PASCAL 
E)  MATHEMATICIAN AGNESI

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

Evaluate the determinant of the matrix below.

Find A².(Note: A² = AA.)

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

Use the matrix capabilities of a graphing utility to evaluate the expression.

Given , find

Write a cryptogram for the message "TWO IF BY LAND" using the matrix Show all your work.

Write the augmented matrix of the system of equations below.

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

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

If possible, find AB.

Given , use to decode the following cryptogram:

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Sequences, Series, and Probability

Filters

Exam 6: Matrices and Determinants

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

Evaluate the determinant of the matrix below.

Find A2.(Note: A2 = AA.)

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

Use the matrix capabilities of a graphing utility to evaluate the expression.

Given , find

Write a cryptogram for the message "TWO IF BY LAND" using the matrix Show all your work.

Write the augmented matrix of the system of equations below.

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

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

If possible, find AB.

Given , use to decode the following cryptogram:

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Sequences, Series, and Probability

Filters

Find A².(Note: A² = AA.)