Question 1

Write the augmented matrix for the system.
-

Accepted Answer

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

Question 2

Find the inverse of the matrix, if possible.
-

Accepted Answer

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

Question 3

Determine the size of the matrix.
-[6]

Accepted Answer

A)  1 
B)  0 × 0 
C)  0 
D)  1 × 1 
A)  1 
B)  0 × 0 
C)  0 
D)  1 × 1

Question 4

Find the minor for the element in the first row and second column of the given matrix.
-

Accepted Answer

A)  105 
B)  63 
C)  303 
D)  -84 
A)  105 
B)  63 
C)  303 
D)  -84

Question 5

Find the determinant of the given matrix.
-

Accepted Answer

A)  80 
B)  -80 
C)  35 
D)  -125 
A)  80 
B)  -80 
C)  35 
D)  -125

Question 6

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.)
-2.1x - 2.8y - 5.0z = 2.2 4.9x - 3.2y - 1.8z = -4.2
2.1x - 1.2y - 4.6z = 11.1

Accepted Answer

A)  {(2.1, 6.3, -3.1)} 
B)  {(4.3, 12.7, -6.2)} 
C)  {(8.6, 25.3, -12.3)} 
D)  {(10.7, 31.7, -15.4)} 
A)  {(2.1, 6.3, -3.1)} 
B)  {(4.3, 12.7, -6.2)} 
C)  {(8.6, 25.3, -12.3)} 
D)  {(10.7, 31.7, -15.4)}

Question 7

Determine the size of the matrix.
-

Accepted Answer

A)  1 
B)  3 
C)  1 × 3 
D)  3 × 1 
A)  1 
B)  3 
C)  1 × 3 
D)  3 × 1

Question 8

Write the augmented matrix for the system.
-

Accepted Answer

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

Question 9

Solve the problem.
-Sara works at a fast food restaurant. On one day she sold 17 double hamburgers, 23 fish sandwiches, 49 orders of French fries, 61 small drinks, 41 medium drinks, and 57 large drinks. On the next day she sold 80 double
Hamburgers, 16 fish sandwiches, 20 orders of French fries, 85 small drinks, 26 medium drinks, and 32 large
Drinks. Write this information in a 2x6 matrix.

Accepted Answer

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

Question 10

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 11

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.
-A is 3 × 1, B is 3 × 1.

Accepted Answer

A)  AB is 1 × 3, BA is 3 × 1. 
B)  AB is 3 × 3, BA is 1 × 1. 
C)  AB is 3 × 1, BA is 1 × 3. 
D)  AB is undefined, BA is undefined. 
A)  AB is 1 × 3, BA is 3 × 1. 
B)  AB is 3 × 3, BA is 1 × 1. 
C)  AB is 3 × 1, BA is 1 × 3. 
D)  AB is undefined, BA is undefined.

Question 12

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.
-A is 3 × 3, B is 3 × 3.

Accepted Answer

A)  AB is 3 × 3, BA is 3 × 3. 
B)  AB is 1 × 1, BA is 1 × 1. 
C)  AB is 6 × 3, BA is 6 × 3. 
D)  AB is 3 × 6, BA is 3 × 6. 
A)  AB is 3 × 3, BA is 3 × 3. 
B)  AB is 1 × 1, BA is 1 × 1. 
C)  AB is 6 × 3, BA is 6 × 3. 
D)  AB is 3 × 6, BA is 3 × 6.

Question 13

Solve the system using Gaussian elimination.
-4x + 4y = -4 2x - 2y = -10

Accepted Answer

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

Question 14

Find the values that make the equation true.
-[7 b 5] + [a 8 c] = [3 8 -7]

Accepted Answer

A)  a = 10, b = 16, c = -2 
B)  a = -4, b = 0, c = -12 
C)    
D)  a = 4, b = 0, c = 12 
A)  a = 10, b = 16, c = -2 
B)  a = -4, b = 0, c = -12 
C)    
D)  a = 4, b = 0, c = 12

Question 15

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.)
-2.2x + 2.4y - 1.4z = 2.7 5.1x - 6.9y + 0.2z = -3.9
4.6x + 4.2y + 3.2z = 10.4

Accepted Answer

A)  {(2.6, 4.3, 3.7)} 
B)  {(0.3, 0.5, 0.5)} 
C)  {(0.6, 1.1, 0.9)} 
D)  {(1.3, 2.1, 1.8)} 
A)  {(2.6, 4.3, 3.7)} 
B)  {(0.3, 0.5, 0.5)} 
C)  {(0.6, 1.1, 0.9)} 
D)  {(1.3, 2.1, 1.8)}

Question 16

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.
--4x - y + 9z = 66 -4x + 5y + 8z = 75
5x - 2y + z = 18

Accepted Answer

A)    
B)  {(3, 3, 9)} 
C)  {(3, 9, 3)} 
D)  {(-3, 3, 6)} 
A)    
B)  {(3, 3, 9)} 
C)  {(3, 9, 3)} 
D)  {(-3, 3, 6)}

Question 17

Solve the problem.
-A $112,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The bond and CD investment must equal the mortgage investment. To earn an $8760 annual income from the investments,
How much should the bank invest in bonds?

Accepted Answer

A)  $16,000 
B)  $18,000 
C)  $38,000 
D)  $56,000 
A)  $16,000 
B)  $18,000 
C)  $38,000 
D)  $56,000

Question 18

Use Cramer's rule to solve the system.
-

Accepted Answer

A)  {(-5, 3)} 
B)  {(-3,-5)} 
C)  {(3, -5)} 
D)  {(5,-3)} 
A)  {(-5, 3)} 
B)  {(-3,-5)} 
C)  {(3, -5)} 
D)  {(5,-3)}

Question 19

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.
-A is 2 × 1, B is 1 × 1.

Accepted Answer

A)  AB is 2 × 1, BA is undefined. 
B)  AB is 2 × 2, BA is 1 × 1. 
C)  AB is undefined, BA is 1 × 2. 
D)  AB is 1 × 2, BA is 1 × 1. 
A)  AB is 2 × 1, BA is undefined. 
B)  AB is 2 × 2, BA is 1 × 1. 
C)  AB is undefined, BA is 1 × 2. 
D)  AB is 1 × 2, BA is 1 × 1.

Question 20

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

Accepted Answer

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

Write the augmented matrix for the system. -

Find the inverse of the matrix, if possible. -

Determine the size of the matrix. -[6]

Find the minor for the element in the first row and second column of the given matrix. -

Find the determinant of the given matrix. -

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -2.1x - 2.8y - 5.0z = 2.2 4.9x - 3.2y - 1.8z = -4.2 2.1x - 1.2y - 4.6z = 11.1

Determine the size of the matrix. -

Write the augmented matrix for the system. -

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

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 3 × 1, B is 3 × 1.

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 3 × 3, B is 3 × 3.

Solve the system using Gaussian elimination. -4x + 4y = -4 2x - 2y = -10

Find the values that make the equation true. -[7 b 5] + [a 8 c] = [3 8 -7]

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -2.2x + 2.4y - 1.4z = 2.7 5.1x - 6.9y + 0.2z = -3.9 4.6x + 4.2y + 3.2z = 10.4

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. --4x - y + 9z = 66 -4x + 5y + 8z = 75 5x - 2y + z = 18

Solve the problem. -A $112,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The bond and CD investment must equal the mortgage investment. To earn an $8760 annual income from the investments, How much should the bank invest in bonds?

Use Cramer's rule to solve the system. -

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 2 × 1, B is 1 × 1.

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

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Exam 9: Matrices and Determinants

Write the augmented matrix for the system. -

Find the inverse of the matrix, if possible. -

Determine the size of the matrix. -[6]

Find the minor for the element in the first row and second column of the given matrix. -

Find the determinant of the given matrix. -

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -2.1x - 2.8y - 5.0z = 2.2 4.9x - 3.2y - 1.8z = -4.2 2.1x - 1.2y - 4.6z = 11.1

Determine the size of the matrix. -

Write the augmented matrix for the system. -

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

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 3 × 1, B is 3 × 1.

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 3 × 3, B is 3 × 3.

Solve the system using Gaussian elimination. -4x + 4y = -4 2x - 2y = -10

Find the values that make the equation true. -[7 b 5] + [a 8 c] = [3 8 -7]

Use the determinant feature of a graphing calculator to solve the system by Cramer's rule . (Round to one decimal place.) -2.2x + 2.4y - 1.4z = 2.7 5.1x - 6.9y + 0.2z = -3.9 4.6x + 4.2y + 3.2z = 10.4

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. --4x - y + 9z = 66 -4x + 5y + 8z = 75 5x - 2y + z = 18

Solve the problem. -A $112,000 trust is to be invested in bonds paying 8%, CDs paying 6%, and mortgages paying 9%. The bond and CD investment must equal the mortgage investment. To earn an $8760 annual income from the investments, How much should the bank invest in bonds?

Use Cramer's rule to solve the system. -

The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist. -A is 2 × 1, B is 1 × 1.

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

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

Filters