Linear Algebra Question Paper
Linear Algebra
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2012
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UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 1101: LINEAR ALGEBRA
DATE: APRIL 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Let A = {-1,0,2,3,6,11}, B = {- 2,-1,0,4,28,108}and f : A? B is a function given
by f (x) = x2 - x - 2 find the co-domain and range of f . (4 Marks)
b) Each of the 50 students in the first year of KCA University’s Computer Science Department
studies at least one of the subsidiary subjects: mathematics,Electronics and accounting. Given that
30 study mathematics, 18 study Electronics, 26 study accounting, 9 study mathematics and
electronics, 16 study Mathematics and accounting, and 8 study electronics and accounting, 47
study at least one of the three subjects.
(i) How many students study none of the three subjects
(ii) How many students study all of the three subjects
(iii) How many students study mathematics and electronics but not accounting
(iv) How many students study mathematics but neither electronics nor accounting
(8 Marks)
c) Construct a truth table for the statement form
{p ?(q ? r)}?{(p ? q)?r} (6 Marks)
d) Test the validity of the following argument:
‘If you are eligible for admission then you must be under 25 and if you are not under 25 then you do
not qualify for scholarship. Therefore if you qualify for a scholarship then you are eligible for
admission. (6 Marks)
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e) Use Venn diagram to illustrate the set Ac n(B - C) (3 Marks)
f) How many 5-digit numbers Greater than 30000 can be formed using the figures 0,1,2,3,5,7,8; if
each digit is only used once (3 Marks)
QUESTION TWO
a) Given that f (x) = x2 +1 and g(x) = x -1 .Find fog and gof (4 Marks)
b) Which of the following relations are functions? Give reason for your answer
i. {(5,1), (5,2),(5,3),(5,4)}
ii. {(4,1),(3,2), (2,3),(1,4)}
iii. {(1,2),(2,3), (2,4),(1,5)}
iv. {(1,2),(2,3),(3,4)} (8 Marks)
c) Use inverse method to solve the systems of equations
2x + y - z = 5
x + y +z = 1
-x + 2y +2z = -4 (8 Marks)
QUESTION THREE
a) Consider the following propositions:
p : Mathematicians are generous.
q : Spiders hate algebra.
Write the compound propositions symbolized by:
i) p ? ¬q
ii) ¬(q ? p)
iii) ¬p ?q
iv) ¬p ?¬q (6 Marks)
b) Prove by induction that ( )
6
12 22 32..... 2 ( +1) 2 +1
+ + + n = n n n (6 Marks)
c) Let A = {1,2,3,4}, R = {(1,1),(1,3),(1,4),(2,2),(2,4), (3,4)} and
S = {(1,2),(2,3),(2,4),(3,1),(3,4)}.Find SoR, RoR and RoS (8 Marks)
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QUESTION FOUR
a) Solve the following system of equations
6x +y -z = 1
-2x+ 3y +4z = 4
9x +2y -2z = -1
Using:
i) Cramers rule
ii) Elimination method (12 Marks)
b) Let R = {(a, a), (a, b), (a, c), (b, b), (b, c)} be a relation on the set
{a, b, c, d}. What is the minimum number of elements which need to
be added to R in order that it becomes:
i) Reflexive;
ii) Symmetric;
iii) Anti-symmetric;
iv)Transitive? (8 Marks)
QUESTION FIVE
a) Define the following as used in set algebra
i. A set
ii. Empty set
iii. Power set
iv.complement of a set A (4 Marks)
b) Suppose A = {1,2}and B = {2,3} find the power set of A× B (5 Marks)
c) S how that {x : 2x2 + 5x - 3 = 0}? {x : 2x2 + 7x + 2 = 3 x} (4 Marks)
d) Evaluate without using a calculator
i)
5!
8! (2 Marks)
ii) 2
7P (2 Marks)
iii) 1
5
4
11C × C (3 Marks)
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