ITI 111 Spring 2011. Exam 2
Vectors:
If the vectors
(2,4, 3,6)
(0,2,1,5)
a
b
are as indicated, what are the values of
1.
a
a.
65 b. 6.86 c. 9 d. 4.34
2.
b
a.
5.39 b. 10 c. 29 d. 2.83
3.
<ab>
a.
94 b. 16 c. 1,440 d. 35
4.
cos(angle between a and b)
a.
.37 b. .80 c. .02 d. .14
5.
angle between a and b (in degrees)
a.
82 b. 68 c. 88 d. 36
Matrices
If the matrices are as indicated here
01
1
3
2
4
2
3 1 4
1
1
0
2
5 ;
;
1
5 ;
2 5
2
0
0
8
1
2
3
2
11
A
B
C
D
6. Which of these is a 2x3 matrix:
A
B
C
D
E=none of them
7. Which of these is a 2x4 matrix?
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B
C
D
E=none of them
8. Which of these products can be computed, according to the laws of matrix
multiplication:
AA
AB
AC
AD
BA
BB
BC BD
;
;
;
TT
B A
BD
DB
DD
[Please circle all the correct possibilities]
9. Which of these products can have an element that is the (3,4) element of the product.
[That is, if we call the product matrix P, the element that is indexed as
34
P
??
AC
BC
BD
;
;
;
B A
BD
DB
DD
10. What is the actual value of the element
3,4
P
Semantic Bases: If the Matrix relating terms to concepts is given by:
Terms
Concept
young
tea
tax
lab
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 Fall '09
 Boros
 Search Engines, BB BC BD, BC BD BT, Concept young tea, BA BB BC

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