Math 113 - 0203       Exam 3      Friday 8-23-2002	Name_________________________

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.

for # 1-7, solve the following systems or state that there is no solution:

1. (10 pts)	2x + y = 4
		y = (x^2) - 9x + 14

2. (10 pts)	x   +   y   +   z   =  7
		x   +  2y  +  2z  = 10
		2x +  3y   - 4 z  =  3

3. (10 pts)	7x - 3y = -11
		5x + 4y = -14

4. (10 pts)	 x   -  y   + 3z =  4
		4x  - 2y  +  z  =  3
		6x  - 2y  - 4z  = -2

5. (10 pts)	2x + 3y        = 7
		3x + 2y - z   = 1
		         y + z   = 5
		 x   - y  + 2z = 0

6. (10 pts)	3x  -  y   +  z  =  1
		 x  + 2y  -   z  =  4
		2x  - 3y  + 2z =  5

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.

8. (6 pts) Consider the system of equations
	x + 3y - 4z = 5
	2x + y        = -2
	x - 4y + z   = 1
	Write the x-cofactor matrix for this system and find its determinant.

9. (6 pts) Consider the system of equations
	x - 2y + z = 4
	3x + 2y - 3z = 0
	x + cy - 2z = 10
	where c is some constant.  For what value of c is the system degenerate?

10. (4 pts) A linear system consists of 4 equations in 6 variables.  What are the possible number of solutions to this
	system?

11. (8 pts) Find the area of the triangle with vertices at (0,3), (-4,7), and (3,8).

12. (6 pts) A system of two equations consists of one quadratic and one circle.  There are exactly 3 solutions to the
	system.  On the coordinate axes below, draw a possible graph of the system.

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.

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