MATH 141 Fall 2010 - Dr. Oksana Shatalov
STAPLE YOUR WORK
FIRST NAME Row# LAST NAME
Due Thursday 9/16 at the beginning of class.
• If turned in later than 10 minutes into class, 5 points off. No papers will be accepted after class.
• If you turn it in to my office (Blocker 629F), place it in my mailbox (Blocker 603) or e-mail a PDF-version to me, make sure you do it before 8:50am, Thursday 9/16/2010.
• You MUST show ALL your work to get full credit. Just writing the answers down is not enough. Even if you use your calculator, write down the preliminary work.
• Your work must be neat, easy to follow. BOX YOUR FINAL ANSWERS.
• You may use notes and textbook, but not the help of anything else.
On my honor, as an Aggie, I certify that the solution submitted by me is my own work. I had neither given nor received unauthorized aid on this work.
Signature:
1. The sizes of matrices A, B, C, D are given in the table:
A B C D
4 × 4 7 × 7 4 × 7 7 × 4
Determine if the following matrices are defined. If yes, find the size, if not, explain why.
(a) BDC
(b) BC T
(c) 7 B + I
7
D
(d) A − 1 C + BD
(e) C − 1
1

2.
A =

6 6
6 28 x − 4

, B =
" y − 1 1 9
4 5 2 z + 1
#
, C =

6 3 u
0 1
− 10 − 1

(a) Find
2 a
11
+ 3 b
21
− 5 c
32
=
(b) Solve for u, x, y , and z in the following matrix equation:
A T − 6 B = − 2 C T
2

3. Given system of linear equations:
2 x
1
− x
1 x
1
+ x
3
+ 12 x
2
4 x
2
+ 3 x
2
+ x
4
=
= x
3
= 7 x
3
5
−
− x
= 2010
4
5
Find the matrices A, B, X so that the given system will be equivalent to the matrix equation
AX = B . For each matrix indicate its size.
4. Alex is printing 6000 copies of a document using two printers. During the process, first printer gets a paper jam and prints only half as many copies as second printer. Write a system of equations you could use to determine the number of copies each printer produces.(Be sure that the variables are defined.)
3

5. Matrix A below gives the percentage of eligible voters in a city, classified according to party affiliation and age group:

0 .
50 0 .
30 0 .
20

A = 0 .
45 0 .
38 0 .
17
0 .
38 0 .
52 0 .
10 where rows 1 , 2&3 represent Under 35, 35-55 and over 55, respectively. Columns 1 , 2&3 represent
Democrat, Republican and Independent, respectively. The city currently has 28 , 000 eligible voters under the age of 35. They have 44 , 000 eligible voters between 35-55 years of age, and
18 , 000 eligible voters over 55 years old. Find the matrix B representing the population of eligible voters. Then use it to find a matrix giving the total number of eligible voters in the city who vote Independent.
4