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Linear Algebra Question Paper

Linear Algebra

Course:Diploma In Information Technology

Institution: Kca University question papers

Exam Year:2010

UNIVERSITY EXAMINATIONS: 2008/2009
STAGE I EXAMINATION FOR DIPLOMA IN INFORMATION
TECHNOLOGY
DIT 101: LINEAR ALGEBRA
DATE: APRIL 2010 TIME: 1½HOURS
INSTRUCTIONS: Answer any THREE questions
Question One.
a) Suppose ?={1,2,3,4,5,6,7,8,910} is the universal set and that A={x:x=6},
B ={x: 4=x=9},C={1,3,5,7,9}, D={2,3,5,7,8}.
i. A??B [3 Marks]
ii. B??C [2 Marks]
iii. AnB [3 Marks]
iv. D??C [2 Marks]
v. A\B [2 Marks]
b) Define the following terms with respect to set theory.
i. Universal set
ii. Proper subset
iii. Union of sets
iv. Intersection of sets [4 Marks]
c) Test the validity of the following:
P1: All politicians are married.
P2: Senator Harris is a politician.
P: Therefore, Senator Harris is married. [4 Marks]
2
Question Two
a) A class has 175 students. The following is the description of students studying one or more of
the following subjects in this class. Mathematics 100, physics 70,chemistry 46, mathematics
and physics 30, mathematics and chemistry 28, physics and chemistry 23,mathematics, physics
and chemistry 18.Using a Venn diagrams determine.
i. The number of students enrolled in at least one subject
ii. The number of students taking none of the three subjects
iii. The number of students enrolled in chemistry and mathematics but not physics
iv. The number of students enrolled in chemistry and physics but not mathematics
v. The number of students enrolled in physics and mathematics but not chemistry
vi. The number of students enrolled in chemistry alone
vii. The number of students enrolled in physics alone
viii. The number of students enrolled in mathematics alone. [9 Marks]
b) Given that A={1,2,3}, B={x,y} Find:
i. A×B
ii. B×A
iii. B×B [6 Marks ]
c) Given the matrix A= ??
i. AT [2 Marks]
ii. AB [3 Marks]
Question Three
a) A box contains two white socks, two blue socks and two red socks .Two socks are drawn from
the box at random. Find the probability that they are a match. [6 Marks]
b) Compute the determinant of the matrix
3 - 2 1
1 2 1
7 6 5
[6Marks]
c) A bag contains six white marbles and five red marbles .Find the number of ways four marbles
can be drawn from the bag if:
i. The marbles can be of any color [2 Marks]
3
ii. Two marbles must be red and the other two must be white [3 Marks]
iii. All the marbles must be of the same color [3 Marks]
Question Four
a) Given that u=(1,-2,4) v=(3,5,1) and w=(2,1,-3).Find:
i. 3u-2v
ii. 4u-v-3w [8 Marks]
b) Verify that the proposition p ? ¬ (p ?q) is a tautology [8 Marks]
c) In how many ways can a committee consisting of three men and two women be chosen from
seven men and five women? [4 Marks]
Question Five
a) Let V={1,2,3,4} f={(1,3),(2,1),(3,4),(4,3)} and g={(1,2),(2,3),(3,1),(4,1)} find:
i. f og [3 Marks]
ii. gof [3 Marks]
b) Find the domain of each of the following functions:
ii. f (x) = 25 - x2 [3 Marks]
iii. f (x) = x2 - 3x - 4 [3 Marks]
c) Prove that 2+4+6+…..+2n = n(n+1). [5 Marks]

Linear Algebra Question Paper

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