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1. Which operation was performed on the matrix on the left below to yield the matrix on the right?
2. Which of these properties is true for matrix addition but not matrix multiplication?
A. It’s associative.
B. Some matrices don’t have inverses.
C. There’s an identity.
D. It’s commutative.
3. Graph the solution set of the system of inequalities below.
y < −x + 10 y > 3x − 3
4. A steel company produces two types of machine dies, part A and part B. The company makes a $3.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write the objective function that describes the total weekly profit.
A. z = 3x + 6y
B. z = 9(x + y)
C. z = 6x + 3y
D. z = 3(x – 6) + 6(y – 3)
5. A system of equations in x, y, and z was converted into the following augmented matrix. What is the solution to the system?
A. (0,3.6,−5.5)
B. No solution
C. (−1,4,−7)
D. (11,−7,−47)
6. Solve the system below by the method of your choice. Identify systems with no solution and systems with infinitely many solutions using set notation to express their solution sets.
y = 6 − 2x
4x + 2y = 12
A. {(5, –4)}
B. {(x, y)|2x + y = 6}
C. Ø
D. {(0, 6)}
7. Which of the following augmented matrices represents a dependent system?
8. Use the addition method to solve the system below.
x + 3y = 8
−2x + 2y = 16
A. {(4, 5)}
B. 0
C. {(–5, 5)}
D. {(–4, 4)}
9. Compute the optimal traffic flow along each of the four roads marked x, y, z, and w in the diagram of the city block below.
A. There's one correct answer, which is x = 400, y = 600, z = 200, w = 900.
B. There's no solution, because the system is dependent.
C. There's one correct answer, which is x = 500, y = 500, z = 100, w = 1900.
D. There are infinitely many correct answers, one of which is x = 400, y = 600, z = 200, w = 900.
10. Use the addition method to solve the system below.
x − 2y = −14
2x − 3y = −22
A. {(2, 7)}
B. Ø
C. {(−2, 6)}
D. {(−3, 7)}
11. Write the form of the partial fraction decomposition of the rational expression below. It's not necessary to solve for the constants.
12. Solve for x in
A. 1
B. 2
C. 0
D. −1
13. Solve the system below by the method of your choice.
x3 + y = 0
8x2 − y = 0
A. {(0, 0), (8, –512)}
B. {(0, 0), (–8, 64)}
C. {(0, 0), (–8, 512)}
D. {(–1, 1), (–8, 512)}
14. After computing the determinants required by Cramer's Rule for a system of three equations in three variables, we obtained the following values. What's the solution to the system?
15. Classify the system x + y + z = 1, x − y − z = 2.
A. It has fewer equations than variables, but may still have a unique solution.
B. It has fewer equations than variables, and therefore it is inconsistent.
C. It has fewer equations than variables, and therefore it has infinitely many solutions.
D. It has a unique solution, (1.5,1.0, −1.5).
16. Which one of the following ordered pairs is a solution of the system below?
x + y = 5
x − y = 1
A. (3, 2)
B. (3, −2)
C. (−3, 2)
D. (−3, −2)
17. A steel company produces two types of machine dies, part A and part B, and is bound by the following constraints:
• Part A requires 1 hour of casting time and 10 hours of firing time.
• Part B requires 4 hours of casting time and 3 hours of firing time.
• The maximum numbers of hours per week available for casting and firing are 100 and 70, respectively.
• The cost to the company is $0.75 per part A and $3.00 per part B. Total weekly costs can't exceed $45.00.
Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write a system of three inequalities that describes these constraints.
18. Write the partial fraction decomposition of the rational expression below.
19. Compute
A. −16
B. −19
C. −18
D. −17
20. Solve the system below by the addition method.
x2 + y2 = 9
x2 − y2 = 9
A. {(3, 0)}
B. {(3, 0), (–3, 0)}
C. {(0, 3), (0, –3)}
D. {(0, 3)}
