Spring 2016 Math 166
2
Week in Review XI
1. TRUE ORFALSE: The
 inverse of
courtesy: David J. Manuel
A
(covering Sections 5.1-5.3 and Exam III)
1
#
"
w x
y z
#
"
=
2 −3
0 5
# "
3y −2
2x 4
+
−2 −y
−3 5x
#
"
=
−5 2
−5 13
−5x − 2y − 2z = 10
2x + y = 7
x + z = −5
#
ab
b2
, what is A2 ?
2
−a −ab
3. Find
the inverse
of the matrix B =
#
"
2 −6
−3 9
4. Gig-Em-Byte Computers sells ve dif-
ferent computer models through three
stores in the greater Houston area.
The inventory of each model at each
store is summarized in matrix I :
A
B C D E
4 2 3 7 1
I= 

 2 3 5 0 6 
10 4 3 4 3






W
$700
$1400
$1800
$2700
$3500
R
$840
$1800
$2400
$3300
$4900







or explain why it does not
exist.
Store 1
Store 2
Store 3
3
Wholesale and retail values of each
model computer are summarized in
matrix V :

=
in matrix form, nd A−1 , and use it to
solve the system.
3. If a "and b are nonzero
numbers and
#
A=
is A−1
2. Write the system of equations below
#
2. Find x and y such that
"
=
0 0
1
0 
.
b
1
0 0 c
1. Find w, x, y, and z such that
4 −2
+2
−3 0
a 0 0
0 b 0 

0
0
c



 1
 a
 0
Section 5.1-5.2
"
Section 5.3
Exam III Review (F.1-F.4;
4.3-4.4)
1. You agree to a one-month simple inter-
est loan at an annual rate of 15% and
pay back $486 at the end. How much
principal do you receive?
A
B
C
D
E
2. Determine which investment is better:
9% per year compounded quarterly, or
9.25% per year compounded annually?
(a) What is the retail value of the inventory
at store 2?
(b) What is the wholesale value of the inventory at store 3?
3. You sold a stock for $17,388 that you
bought three years ago for $12,900. To
the nearest 0.1%, what is your annual
compounded rate of return?
1
4. Suppose it costs $20,000 per year to at-
6. At 47, you decide to invest in an IRA.
(a) Assuming 3% per year ination, what
will be the annual cost to attend A&M
when your child turns 18?
(a) How much money should be in the IRA
when you retire?
(b) How much should you deposit into the
IRA each quarter for the next 20 years
to achieve this goal?
(b) You and the grandparents decide to put
$200/month (combined) into a college
fund which averages 8% per year compounded monthly. How much money
will the fund have when your child turns
18?
7. A plush toy manufacturer makes
tend Texas A&M when your rst child
is born.
You want to deposit money each quarter for the next 20 years so that, when
you retire then, you can make quarterly withdrawals of $9,000 for the next
10 years. The IRA earns 7% per year
compounded quarterly.
Chewbacca, Ewok, and Jar-Jar plush
toys. Each Chewbacca requires 3
square feet of plush, 500 cubic inches
of stung, and 25 pieces of trim. Each
Ewok requires 1.5 square feet of plush,
200 cubic inches of stung, and 10
pieces of trim. Each Jar-Jar requires
2 square feet of plush, 300 cubic inches
of stung, and 15 pieces of trim. The
manufacturer has 3,500 square feet of
plush, 500,000 cubic inches of stung,
and 25,000 pieces of trim. How many
of each type of toy could they manufacture?
5. You purchase a new home for $200,000,
putting 10% down and nancing the
rest at 4.5% per year compounded
monthly for 30 years.
8. In addition, the manufacturer needs to
make twice as many Ewoks as Jar-Jars.
How many of each type of toy could
they manufacture now?
(a) What are your monthly payments on the
mortgage?
(b) How much of your rst month's payment
goes toward the principal?
(c) What is the equity in your home after 10
years?
(d) How much of the next payment (after
the 10 years) goes toward the principal?
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