Mathematical Investigations II
Matrices and Geometric Transformations Exam
Name:_________________________
Since the use of a calculator would only distract the knowledgeable student on this exam, do not use
them. Justification of your work is important and expected.
I M S
1.
2.
A
The vertex matrix of quadrilateral IMSA is: 0 3 2 1
0 1 5 1 


a)
Determine the area of IMSA.
b)
Write the matrix equation which translates IMSA 5 units to the left and up 4 to IMSA .
c)
Write the matrix equation which rotates IMSA 270 counter-clockwise about the origin
IMSA .
 x  6 y  3
Given the system of equations: 
2 x  5 y  11
a.
Write a matrix equation that corresponds to the system.
b.
Solve the system for  x, y  .
p. 1 v.2
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onto
3.
The dimensions of matrix A are 96. What should the dimensions of matrix B be
so that both AB and BA can be computed?
4.
At Morgan's Fine Cuisine, meals are served a la carte. That is,
each item on the menu is priced separately. Jackie and Ted Parris
went to Morgan's with their young daughter Katie to celebrate her
birthday. Jackie (J) and Ted (T) ordered prime rib (PR), side
dishes (S) and rolls (R), while Katie (K) only ordered sides and
rolls. Their order is organized in the matrix at the right:
a.
PR
J 1
T 1
K 0
S R
2 1
4 3 
3 2 
How many side dishes did Ted order?
Prime rib costs $23, side dishes are $8 each, and rolls are $1 each.
b.
Set up a matrix equation that shows how much each person's meal cost. Be sure to label
rows and columns.
c.
Using your data from part b, how much was the Parris family's total bill before tax and tip?
p. 2 v.2
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5. To the right is a graph representing the bus routes in Texas for the Texas Ranger Bus-lines.
a) Complete the adjacency matrix (Routes)
describing the cities connected by these routes.
L
Routes =
L
O 
S

R 
O
S
Odessa
San
Antonio
R






Liberty
Rosebud
b) What is the meaning of the entry in Row 2, Column 3 of the matrix Routes4 ?
c) Is it true that Routes  RoutesT ? Why or why not?
p. 3 v.2
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6.
Perform the matrix operations below. If it is not possible to carry out the operation, write
"impossible" and explain why.
5 0
 3 4




a)
 7 1  2   2 0  
 2 8 
 1 6 
 2 6 3  1 5
b) 


 1 9 2   3 4 
 5 3
 3 1 7  

c) 
   0 8 =

6
2

1

 
 4 1 
 1 5  2 6 3
d) 

 
 3 4   1 9 2 
e) Solve for x:
5 x
1
2
 x . Show work clearly.
p. 4 v.2
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