Let 
.
Compute the inverse of 
(Note: four points for
either product correct; four more for the other, and four more for the
difference. Then thirteen for the inverse completely correct.)
Let 
be events in a sample space S; assume
that 
and that 
Letting
(and a Venn diagram if
you
wish), set up a system of three equations in the unknowns 
and solve using row operations. Then compute 
Solve the following system of equations completely using matrix row
operations. Does it have no solution, one solution, or infinitely
many? 
A small toy company is building airplanes and boats. Each airplane is
made using four ounces of plastic and one ounce of aluminum. Each
boat is made entirely of aluminum and requires two ounces. The profit
on each toy, of either type, is three dollars. The resources
available before shutting down for the holidays are 120 ounces of
plastic and 100 ounces of aluminum. How many of each toy should be
manufactured to maximize profits? (Show the profit at every corner!)
For what values of a does the system
have a solution for x and y?
