Calculus and Linear Algebra (GSDR2107)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 200
Year: 2017
School/Faculty: HITL
DEPARTMENT: General Studies LECTURER(S): Dr. KAMEUGNE
Level: 1 FIRST SEMESTER EXAMINATIONM Academic Year: 2016/2017
COURSE CODE: TLGS 1107 COURSE TITLE: CALCULUS AND LINEAR ALG.
DATE: HALL: TIME: 2 hrs
Instructions: Answer all questions
THE UNIVERSITY OF BAMENDA
P.O BOX 39 Bambili
REPUBLIC OF CAMEROON
Peace-Work-Fatherland
0 .
. 17 0
r.
Part A/CALCULUS
Exercise 1 (20 marks) Consider the initial equation
(5 marks)
1) Solve the homogenous equation xy' + 2y = 0 associated to this equation (5 marks)
2) Using the variation of the constant, show that the complex solution is y=
where C
(10 marks)
3) Determine the value of the initial equation (5 marks)
Exercise 2 (15 marks) Consider the function
1)
Factorize the quadratic polynomial
2)
Find the partial-fraction decomposition of f(x).(Ind. Determine the reals A, B such that
!
)
3)
Find f(x)dx
Part B/ LINEAR EQUATION
Exercise 3 (20 marks) Consider the linear system of equations
"
#$
%
#$
&
#$
1. Write down the augmented matrix of the system (3 marks)
2. Use Gaussian elimination to bring the augmented matrix to row echelon form and, as in the
lectures, indicate which elementary row operations are used at each step. (7 marks)
3. Then continue and show that the reduced echelon form is (5 marks)
'
(
)
*
+
,
Where a, b and c are real numbers to be determined.
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4. Identify the leading and the free variables, and write down the solution set of the system. (5
marks)
Exercise 4 (15 marks) Consider the matrix
A = -
&
.
1. Show that A is invertible (5 marks)
2. Compute the inverse of the matrix A. (7 marks)
3. Show that B = -
%
.is the inverse of A (3 marks)
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