Question 1

Solve the system using Cramer's rule and a graphing calculator. (Round to two decimal places.)
--8.18x - 3.36y = 9 -0.06x - 8.09y = 5

Accepted Answer

A)  {(0.85, 0.61)} 
B)  {(-0.61, -0.85)} 
C)  {(-0.85, -0.61)} 
D)  {(0.61, -0.85)} 
A)  {(0.85, 0.61)} 
B)  {(-0.61, -0.85)} 
C)  {(-0.85, -0.61)} 
D)  {(0.61, -0.85)}

Question 2

Find the product if possible.
-

Accepted Answer

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

Question 3

Find the indicated matrix.
-Let B = [-1 4 4 -3]. Find -2B.

Accepted Answer

A)  [2 -8 -8 6] 
B)  [-3 2 2 -5] 
C)  [-2 8 8 -6] 
D)  [2 4 4 -3] 
A)  [2 -8 -8 6] 
B)  [-3 2 2 -5] 
C)  [-2 8 8 -6] 
D)  [2 4 4 -3]

Question 4

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.
-5x + 4y = 8 -4x + 2y = -22

Accepted Answer

A)  {(-3, 4)} 
B)  {(-4, 3)} 
C)  {(3, -4)} 
D)  {(4, -3)} 
A)  {(-3, 4)} 
B)  {(-4, 3)} 
C)  {(3, -4)} 
D)  {(4, -3)}

Question 5

Given matrices A and B, find the indicated matrix if possible.
-A = -1 -2 , B =   Find AB.

Accepted Answer

A)    
B)    
C)  AB is not defined. 
D)    
A)    
B)    
C)  AB is not defined. 
D)

Question 6

Use a graphing calculator to solve the system by finding   . (Round to the nearest integer if necessary.)
-

Accepted Answer

A)  {(1, 9, 3)} 
B)  {(1, -9, -3)} 
C)  {(2, 7, 3)} 
D)  {(9, 3, 9)} 
A)  {(1, 9, 3)} 
B)  {(1, -9, -3)} 
C)  {(2, 7, 3)} 
D)  {(9, 3, 9)}

Question 7

Use a graphing calculator to solve the system by finding   . (Round to the nearest integer if necessary.)
--4x - 6y - z = -45 x - 6y + 3z = -16
6x + y + z = 35

Accepted Answer

A)  {(4, 1, 4)} 
B)  {(5, -4, -1)} 
C)  {(5, 4, 1)} 
D)  {(6, 2, 1)} 
A)  {(4, 1, 4)} 
B)  {(5, -4, -1)} 
C)  {(5, 4, 1)} 
D)  {(6, 2, 1)}

Question 8

Perform the indicated row operation on the given augmented matrix.
-

Accepted Answer

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

Question 9

Determine whether the matrices in each pair are inverses of each other.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 10

For the given matrix A, find -A.
-

Accepted Answer

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

Question 11

Write the matrix equation as a system of equations and solve the system.
-

Accepted Answer

A)  {(7, -7, 3)} 
B)  {(-3, 5, 5)} 
C)  {(-23, 37, 12)} 
D)  {(2, 12, 16)} 
A)  {(7, -7, 3)} 
B)  {(-3, 5, 5)} 
C)  {(-23, 37, 12)} 
D)  {(2, 12, 16)}

Question 12

Find the determinant of the given matrix.
-

Accepted Answer

A)    
B)    
C)  0 
D)    
A)    
B)    
C)  0 
D)

Question 13

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the
matrix product AB, and interpret the significance of the entries of this product.
-

Accepted Answer

A)    The total tuition paid by all 3 students is $3822. 
B)    Tuition for Student 1 is $1251, tuition for Student 2 is $1274, and tuition for Student 3 is $923. 
C)    The total tuition paid by all 3 students is $3973. 
D)    Tuition for Student 1 is $1258, tuition for Student 2 is $1272, and tuition for Student 3 is $937. 
A)    The total tuition paid by all 3 students is $3822. 
B)    Tuition for Student 1 is $1251, tuition for Student 2 is $1274, and tuition for Student 3 is $923. 
C)    The total tuition paid by all 3 students is $3973. 
D)    Tuition for Student 1 is $1258, tuition for Student 2 is $1272, and tuition for Student 3 is $937.

Question 14

Solve the problem.
-At a track meet, Russell ran the first heat of the 100-yd dash in 15.5 sec, Sergy in 15.8 sec, and Omar in 16.2 sec. In the second heat, they got 15.3 sec, 15.4 sec, and 15.7 sec. Write a 3 x 1 matrix giving the changes in times. If
The changes repeat, who will win?

Accepted Answer

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

Question 15

Find the sum, if possible.
-

Accepted Answer

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

Question 16

Determine the row operation that was used on the first matrix to obtain the second matrix.
-

Accepted Answer

The answer of Determine the row operation that was used...

Question 17

Find the indicated matrix.
-  Find C - 4D.

Accepted Answer

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

Question 18

Provide an appropriate response.
-Indicate whether the following statement is true or false.
If a 3 x 3 matrix has two identical rows, but the third row is different from the other two, its determinant equals 0.

Accepted Answer

A) True 
 B)False

Solve the system using Cramer's rule and a graphing calculator. (Round to two decimal places.) --8.18x - 3.36y = 9 -0.06x - 8.09y = 5

Find the product if possible. -

Find the indicated matrix. -Let B = [-1 4 4 -3]. Find -2B.

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. -5x + 4y = 8 -4x + 2y = -22

Given matrices A and B, find the indicated matrix if possible. -A = -1 -2 , B = Find AB.

Use a graphing calculator to solve the system by finding . (Round to the nearest integer if necessary.) -

Use a graphing calculator to solve the system by finding . (Round to the nearest integer if necessary.) --4x - 6y - z = -45 x - 6y + 3z = -16 6x + y + z = 35

Perform the indicated row operation on the given augmented matrix. -

Determine whether the matrices in each pair are inverses of each other. -

For the given matrix A, find -A. -

Write the matrix equation as a system of equations and solve the system. -

Find the determinant of the given matrix. -

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve the problem. -At a track meet, Russell ran the first heat of the 100-yd dash in 15.5 sec, Sergy in 15.8 sec, and Omar in 16.2 sec. In the second heat, they got 15.3 sec, 15.4 sec, and 15.7 sec. Write a 3 x 1 matrix giving the changes in times. If The changes repeat, who will win?

Find the sum, if possible. -

Determine the row operation that was used on the first matrix to obtain the second matrix. -

Find the indicated matrix. - Find C - 4D.

Provide an appropriate response. -Indicate whether the following statement is true or false. If a 3 x 3 matrix has two identical rows, but the third row is different from the other two, its determinant equals 0.

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Exam 9: Matrices and Determinants

Solve the system using Cramer's rule and a graphing calculator. (Round to two decimal places.) --8.18x - 3.36y = 9 -0.06x - 8.09y = 5

Find the product if possible. -

Find the indicated matrix. -Let B = [-1 4 4 -3]. Find -2B.

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. -5x + 4y = 8 -4x + 2y = -22

Given matrices A and B, find the indicated matrix if possible. -A = -1 -2 , B = Find AB.

Use a graphing calculator to solve the system by finding . (Round to the nearest integer if necessary.) -

Use a graphing calculator to solve the system by finding . (Round to the nearest integer if necessary.) --4x - 6y - z = -45 x - 6y + 3z = -16 6x + y + z = 35

Perform the indicated row operation on the given augmented matrix. -

Determine whether the matrices in each pair are inverses of each other. -

For the given matrix A, find -A. -

Write the matrix equation as a system of equations and solve the system. -

Find the determinant of the given matrix. -

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve the problem. -At a track meet, Russell ran the first heat of the 100-yd dash in 15.5 sec, Sergy in 15.8 sec, and Omar in 16.2 sec. In the second heat, they got 15.3 sec, 15.4 sec, and 15.7 sec. Write a 3 x 1 matrix giving the changes in times. If The changes repeat, who will win?

Find the sum, if possible. -

Determine the row operation that was used on the first matrix to obtain the second matrix. -

Find the indicated matrix. - Find C - 4D.

Provide an appropriate response. -Indicate whether the following statement is true or false. If a 3 x 3 matrix has two identical rows, but the third row is different from the other two, its determinant equals 0.

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Trigonometric Identities and Conditional Equations

Applications of Trigonometry

Systems of Equations and Inequalities

The Conic Sections

Sequences, Series, and Probability

Basic Algebra Review

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