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mat_110_college_algebra-written_assignment_5_v1.pdf
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UNIVERSITY OF WISCONSIN COLLEGES ONLINE
MAT 110 College Algebra
WRITTEN ASSIGNMENT 5 – 2012 (Version 1)
INSTRUCTIONS
This assignment can be completed as a MS Word document in conjunction with an equation editor. The document can then be saved either as a MS Word 97-‐2003 document or PDF file and uploaded into the Dropbox in the Course D2L Site. Alternatively, your solutions can be hand written and scanned as a single PDF file and uploaded into the appropriate Dropbox in the Course D2L Site. Before uploading, make sure the file is complete, legible, and has the correct page orientation. You should re-‐space the assignment pages as necessary to allow adequate space to place each answer. For each problem:
• Number and state the problem.
• Clearly show your solution neatly, working step-‐by-‐step down the page.
• Simplify answers within reason. For instance, calculations and fractions should be simplified to their exact values and lowest terms, where possible.
• Not showing your work is not acceptable. If you are confident that a fellow student could
look at the problem and follow your reasoning, then you likely have shown enough work.
• Use correct mathematical notation. Avoid using non-‐standard short-‐hands or abbreviations.
• Use a line across the page showing where the problem ends.
This Written Assignment covers:
• Unit 5: Topic 5.1 Systems of Linear Equations
• Unit 5: Topic 5.2 Matrix Solution of Linear Equations
• Unit 5: Topic 5.3 Determinant Solution of Linear Systems
Work on the relevant exercises as you proceed through the material. DO NOT wait until the last minute to begin the Written Assignment. When you are done, save your work in an easily accessible place.
In addition to the Exercises on the following page, I suggest you try the Exercises listed in the Topics for Unit 3 and check your answers in the book. These Exercises are not collected or graded, but certainly can be discussed with your instructor and will be beneficial preparation for the written assignment.
GRADING: 50 Points Possible
Note: You will be graded not just based on your answer but also on the presentation of how you determined your answer.
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MAT 110 College Algebra-‐Written Assignment 5
Section 1: Individual Answers (40 Points)
In this section you must answer the questions yourself without collaborating with anyone else.
1. Solving the following system of linear equations by graphing.
y = –3x + 5
x – 2y = –3
2. Solve the following system of equations. [Hint: Let t = 1 x
and u = 1 y
.]
1 x + 3 y = 16 5
5 x + 4 y = 5
1 2 3 4 5 6 7 8 -8 -7 -6 -5 -4 -3 -2 -1
8 7 6 5 4
3 2
1
- 8 - 7 - 6 - 5
- 4 - 3 - 2 - 1
x
y
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3. Solve the following system of linear equations.
4x + 3y + z = −8 3x + y − z = −6 x + y + 2z = −2
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4. For certain aircraft there exists a quadratic relationship between an airplane’s maximum speed S (in knots) and its ceiling C, or highest altitude possible (in thousands of feet). The table lists three airplanes that conform to this relationship.
Airplane Max Speed (S) Ceiling (C)
Hawkeye 320 33
Corsair 600 40
Tomcat 1283 50
(a) If the quadratic relationship between C and S is written as C = aS2 + bS + c, use a system of linear equations to determine the constants a, b, and c.
(b) A new aircraft of this type has a ceiling of 45,000 feet. Predict its top speed.
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5. Use the Gauss-Jordan method to solve the following system of equations
x + 3y − 6z = 7 2x − y + z =1 x + 2y + 2z = −1
6. At Everglades Nut Company, 5 lb of peanuts and 6 lb of cashews cost $33.60, while 3 lb of peanuts and 7 lb of cashews cost $32.40. Find the cost of a single pound of peanuts and a single pound of cashews.
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7. Find the value of the determinant
2 1 −1 4 7 −2 2 4 0
8. Use Cramer’s Rule to solve the system of equations
x + y + z = 4 2x − y + 3z = 4 4x + 2y − z = −15
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Section 2: Group Discussion Question (10 Points) Your Group Number: _______________________
This question must be completed as a group discussion. Your discussion should be conducted in your Group Discussion board found under Discussions. Your grade will be based on your participation in your group, on the solution and how it is presented. You need to show all relevant steps required to produce a solution to the question. Only one designated person (Group leader) in the group need submit the group answer to the Discussion Question and upload it as part of their final submission to the Dropbox. Please be sure to identify the group number by placing the number in the space shown above and the members of the group who participated in solving the problem by placing their names in the space provided below.
Group Members Names:
1.__________________________ 2. _________________________ 3. ____________________________ 4. __________________________
There is an alternative method that can be employed to evaluate the determinant of a 3 x 3 matrix A. To apply this method we copy the first and second columns of A to form fourth and fifth columns. The determinant of A is then obtained by adding (or subtracting) the products of the six diagonals as shown below.
(a) Find the determinant 1 3 2 0 2 6 7 1 5
using the diagonal method shown above.
(b) Referring the Part (a). Find the determinant by expanding about Column 1 and using the method of cofactors. Do these methods give the same determinant for 3 x 3 matrices?
