Question 1

Find the values that make the equation true.
-

Accepted Answer

A)  a = -6, b = -13, c = 1, d = 10, e = -15, f = 2 
B)    
C)  a = 4, b = 1, c = -1, d = 4, e = 15, f = 0 
D)  a = 6, b = 13, c = -5, d = -10, e = -3, f = -2 
A)  a = -6, b = -13, c = 1, d = 10, e = -15, f = 2 
B)    
C)  a = 4, b = 1, c = -1, d = 4, e = 15, f = 0 
D)  a = 6, b = 13, c = -5, d = -10, e = -3, f = -2

Question 2

Solve the problem using two linear equations in two variables and Cramer's rule.
-Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is 1400 liters/hr. What is the flow in each pipe?

Accepted Answer

A)  700 liters/hr hot, 467 liters/hr cold 
B)  560 liters/hr hot, 840 liters/hr cold 
C)  467 liters/hr hot, 700 liters/hr cold 
D)  840 liters/hr hot, 560 liters/hr cold 
A)  700 liters/hr hot, 467 liters/hr cold 
B)  560 liters/hr hot, 840 liters/hr cold 
C)  467 liters/hr hot, 700 liters/hr cold 
D)  840 liters/hr hot, 560 liters/hr cold

Question 3

Use Cramer's rule to solve the system.
-2.2x + 1.8y = 15.0 2.9x - 1.5y = 15.9

Accepted Answer

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

Question 4

Determine whether the matrix is invertible by finding the determinant of the matrix.
-

Accepted Answer

A)  Not invertible 
B)  Invertible 
A)  Not invertible 
B)  Invertible

Question 5

Find the values that make the equation true.
-6 p+3 q-7 = k+2 5 -9

Accepted Answer

A)  k = -4; p = -2; q = 2; 
B)  k = 4; p = 2; q = -2 
C)  k = 5; p = -2; q = 0 
D)  k = 2; p = 6; q = -9 
A)  k = -4; p = -2; q = 2; 
B)  k = 4; p = 2; q = -2 
C)  k = 5; p = -2; q = 0 
D)  k = 2; p = 6; q = -9

Question 6

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation.
-3x + 5y = -10 -2x - 4y = 6

Accepted Answer

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

Question 7

Solve the problem.
-The sum of three numbers is 7. The first, minus the second, plus 4 times the third, is 26. The third, plus 4 times the first, plus the second, is 19. What are the numbers?

Accepted Answer

A)  -4, 2, -5 
B)  No solution 
C)  4, 4, -2 
D)  4, -2, 5 
A)  -4, 2, -5 
B)  No solution 
C)  4, 4, -2 
D)  4, -2, 5

Question 8

Use Cramer's rule to solve the system.
-3x + 2y = -3 3x + y = -9

Accepted Answer

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

Question 9

Provide an appropriate response.
-Which of the following are not allowable transformations when the Gaussian elimination method is used to solve a system of linear equations?
(i) A multiple of elements of one row may be added to the
Corresponding elements of any other row.
(ii) Any two columns may be interchanged.
(iii) The elements of any row may be multiplied by the
Corresponding elements of another row.
(iv) All of the elements of any row may be multiplied by
Any nonzero number.

Accepted Answer

A)  (ii), (iii), (iv) 
B)  (ii) 
C)  (ii), (iii) 
D)  (i), (iv) 
A)  (ii), (iii), (iv) 
B)  (ii) 
C)  (ii), (iii) 
D)  (i), (iv)

Question 10

Solve the system using Gaussian elimination.
-8x + 6y - z = 87 x - 3y + 3z = -6
-7x + y + z = -32

Accepted Answer

A)  {(6, 3, 7)} 
B)  {(6, 7, 3)} 
C)    
D)  {(-6, 7, 12)} 
A)  {(6, 3, 7)} 
B)  {(6, 7, 3)} 
C)    
D)  {(-6, 7, 12)}

Question 11

Solve the problem.
-When the owner of a picture framing store took inventory of her unused frames, she found that she had 45 oak-8", 14 oak-12", 47 oak-18", 11 walnut-8", and 10 walnut-18". Write this information as a 2 x 3 matrix.

Accepted Answer

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

Question 12

Perform the indicated operation, if possible.
-

Accepted Answer

A)  10 6 -8 
B)    
C)    
D)    
A)  10 6 -8 
B)    
C)    
D)

Question 13

Use Cramer's rule to solve the system.
-2x + 3y = 27 2x + 4y = 32

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Provide an appropriate response.
-Indicate whether the following statement is true or false.
If every element in one column of a 2 x 2 matrix is 0, but all other elements in the matrix are nonzero, the
determinant of the matrix is 0.

Accepted Answer

A) True 
 B)False

Question 16

Solve the problem using two linear equations in two variables and Cramer's rule.
-A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 5% cement should he mix with 5 bags of 13% cement to produce a mix containing 9% cement?

Accepted Answer

A)  15 bags 
B)  5 bags 
C)  7 bags 
D)  10 bags 
A)  15 bags 
B)  5 bags 
C)  7 bags 
D)  10 bags

Question 17

Find the determinant of the given matrix.
-

Accepted Answer

A)  214 
B)  1150 
C)  262 
D)  -262 
A)  214 
B)  1150 
C)  262 
D)  -262

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Write the augmented matrix for the system.
-

Accepted Answer

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

Find the values that make the equation true. -

Solve the problem using two linear equations in two variables and Cramer's rule. -Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is 1400 liters/hr. What is the flow in each pipe?

Use Cramer's rule to solve the system. -2.2x + 1.8y = 15.0 2.9x - 1.5y = 15.9

Determine whether the matrix is invertible by finding the determinant of the matrix. -

Find the values that make the equation true. -6 p+3 q-7 = k+2 5 -9

Solve the system using the inverse of the coefficient matrix of the equivalent matrix equation. -3x + 5y = -10 -2x - 4y = 6

Solve the problem. -The sum of three numbers is 7. The first, minus the second, plus 4 times the third, is 26. The third, plus 4 times the first, plus the second, is 19. What are the numbers?

Use Cramer's rule to solve the system. -3x + 2y = -3 3x + y = -9

Solve the system using Gaussian elimination. -8x + 6y - z = 87 x - 3y + 3z = -6 -7x + y + z = -32

Solve the problem. -When the owner of a picture framing store took inventory of her unused frames, she found that she had 45 oak-8", 14 oak-12", 47 oak-18", 11 walnut-8", and 10 walnut-18". Write this information as a 2 x 3 matrix.

Perform the indicated operation, if possible. -

Use Cramer's rule to solve the system. -2x + 3y = 27 2x + 4y = 32

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

Provide an appropriate response. -Indicate whether the following statement is true or false. If every element in one column of a 2 x 2 matrix is 0, but all other elements in the matrix are nonzero, the determinant of the matrix is 0.

Solve the problem using two linear equations in two variables and Cramer's rule. -A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 5% cement should he mix with 5 bags of 13% cement to produce a mix containing 9% cement?

Find the determinant of the given matrix. -

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

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

Write the augmented matrix for the system. -

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Exam 9: Matrices and Determinants