MAT183
Name_______________________________
Exam #1
Feb. 13, 2004
Answer ALL questions!
Be sure that your exam has 7 questions!
Show all work.
Little
or no credit will be given for answers without justification!
(1)
(20 pts)
Using the method of Gaussian elimination, solve the following system of
equations.
(You may, of course, check your answer using your calculator, but no credit
will be given for a calculatorbased answer.)
x
+
3
y
+
2
z
=
1
2
x
+
y
−
z
=
2
x
+
y
+
z
=
2
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(2)
(20 pts)
You manage an ice cream factory that makes three flavors:
vanilla, mocha
and strawberry.
Each batch of vanilla uses 2 eggs, 1 cup of milk, and 2 cups of cream.
Each batch of
mocha uses 1 egg, 1 cup of milk and 2 cups of cream.
Each batch of strawberry uses 1
egg, 2 cups of milk, and 1 cup of cream.
How many batches of each flavor should you make in order to use up all of your
ingredients, if you have 350 eggs, 350 cups of milk, and 400 cups of cream?
Set up an equation using matrix multiplication that can be used to solve this problem.
Be
sure to specify what your variables represent.
Use your calculator to solve the equation!
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 Spring '08
 Doerr
 Gaussian Elimination, Savings account, different colored flags

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