Calculus and Linear Algebra (GSDR207)
Higher Institute of Transport and Logistics (HITL)
Semester: Resit
Level: 200
Year: 2017
1
REPUBLIC OF CAMEROON THE UNIVERSITY OF BAMENE
Peace-Work-Fatherland P.O.Box 39 Bambili
HILT RESIT EXAMINATION DEPT. OF GENERAL STUDIES
Academic Year: 2016-2017 CALCULUS AND LIN. ALGEBRA Lect.: Dr. Kameugne R.
TLGS 1107
Instruction: Answer all questions. Duration: 2 hours
CALCULUS
Exercise 1 (20 marks) Consider the function f(x)
1. Determine the reals A, B and C such that f(x) = A +
10 marks
2. Compute f (x)dx
Exercise 2 (20 marks) Consider the initial value equation
1. Solve the homogeneous equation xy' — 3y = 0 associated to this equation 5 marks
2. Using the variation of the constant, show that the complete solution is y =
!
x
7
+ Kx
3
where K"# 10 marks
3. Determine the solution of the initial value equation 5 marks
LINEAR ALGEBRA
Exercise 3 (30 marks) Consider a quadratic polynomial p(x) = ax
2
+bx + c that satisfy p(-1) = 4
p(2) = $% and p(1) =$&
1. Write down a system of linear equations for the coefficients. 5 marks
2. Consider the linear system
'
(
)
*
+
$%
*
+
$&
$)
*
+
(
(a) Write down the augmented matrix of the system. 5 marks
(b) 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. 10 marks
(c) Identify the leading and the free variables, and write down the solution set of the system. 5 marks
3. Factorize the quadratics polynomial p(x)=2x
2
– 5x - 3 5 marks
Exercise 4 (15 marks) Consider the matrix
A = ,
$
$) $&
$ (
-
1. Show that A is invertible 5 marks
2. Use Gauss-Jordan inversion to determine the inverse of the matrix 10 marks
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