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Cell["\<\
Math 113 - 0203 Exam 3 Friday 8-23-2002\t\
Name_________________________\
\>", "Subsection"],
Cell["\<\
Do all problems in the space provided. Mark your final answers clearly and \
write them in the appropriate form. You must show appropriate work to \
receive credit for an answer. You may use a calculator, however you should \
indicate when you use a calculator for complicated operations.\
\>", "Text"],
Cell[TextData[{
"for # 1-7, solve the following systems or state that there is no solution:\
\n\n1. (10 pts)\t2x + y = 4\n\t\ty = ",
Cell[BoxData[
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" - 9x + 14\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t"
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2. (10 pts)\tx + y + z = 7
\t\tx + 2y + 2z = 10
\t\t2x + 3y - 4 z = 3
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t\
\>", "Text"],
Cell["\<\
3. (10 pts)\t7x - 3y = -11
\t\t5x + 4y = -14
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t\
\>", "Text"],
Cell["\<\
4. (10 pts)\t x - y + 3z = 4
\t\t4x - 2y + z = 3
\t\t6x - 2y - 4z = -2
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t\
\>", "Text"],
Cell["\<\
5. (10 pts)\t2x + 3y = 7
\t\t3x + 2y - z = 1
\t\t y + z = 5
\t\t x - y + 2z = 0
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t \
\>", "Text"],
Cell["\<\
6. (10 pts)\t3x - y + z = 1
\t\t x + 2y - z = 4
\t\t2x - 3y + 2z = 5
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t
\t\t\
\>", "Text"],
Cell["\<\
7. (10 pts) Radium is a radioactive substance which decays over time \
according to an exponential model. The half-life of radium is 5500 years. \
Suppose that you start with 20 g of radium. How much radium will be left \
after 15,000 years? Round your answer to one decimal place.
\
\>", "Text"],
Cell["\<\
8. (6 pts) Consider the system of equations
\tx + 3y - 4z = 5
\t2x + y = -2
\tx - 4y + z = 1
\tWrite the x-cofactor matrix for this system and find its determinant.
\t
\t
\t
\t
\t\
\>", "Text"],
Cell["\<\
9. (6 pts) Consider the system of equations
\tx - 2y + z = 4
\t3x + 2y - 3z = 0
\tx + cy - 2z = 10
\twhere c is some constant. For what value of c is the system degenerate?
\t
\t
\t
\t
\t
\t
\t
\t\
\>", "Text"],
Cell["\<\
10. (4 pts) A linear system consists of 4 equations in 6 variables. What are \
the possible number of solutions to this
\tsystem?
\t\
\>", "Text"],
Cell["\<\
11. (8 pts) Find the area of the triangle with vertices at (0,3), (-4,7), and \
(3,8).
\
\>", "Text"],
Cell["\<\
12. (6 pts) A system of two equations consists of one quadratic and one \
circle. There are exactly 3 solutions to the
\tsystem. On the coordinate axes below, draw a possible graph of the system.
\t
\t
\t
\t
\t
\t\
\>", "Text"],
Cell["\<\
BONUS. (8 pts) Suppose that two rows of some 3 x 3 matrix are identical. \
Show that the determinant of this matrix must be 0.
\
\>", "Text"],
Cell["\<\
In the space below, please copy the following and sign your name:
\tI pledge on my honor that I have neither given nor received unauthorized \
aid on this exam.\
\>", "Text"]
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