Calculus and Linear Algebra (GSDR2107)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 200
Year: 2018
1. Consider the following matrices:
,
(a) Compute AC, A + C and C
T
if possible
(b) Compute the determinant of A
(c) Show that the matrix A is invertible and find its inverse.
(d) Consider the following systems of linear equations
i) Write the matrix form of the system
ii) Find the solution of the system using the Cramer formulas or results in
question 1c
2. Are vectors u(1, 2,
) and v(-
) orthogonal? Justify your answer
3. Solve the following differential equation f ′′ - 5f ′ + 6f =0
4. Consider the complex number Z = 2 + 2
a) Find the modulus and the principal argument of Z
b) Write th4ee exponential form of Z
c) Compute Z
81
5. Consider the function (f(x) =
find the limit of the function, if possible, when x tend
to 2. Is the function f continuous at 2? Justify your answer.
6. Consider the following functions: f (x) =
, g(x) = !"#
$
%
a) Compute f ′(x) and g(x)
b) Compute the integral
&
'
(
)
*
FIRST SEMESTER EXAMINATIONS
School/Faculty: HITL Department: General Studies Lecture(s): Dr Fouotsa
Level: 200 Semester: First Academic Year: 2017/2018
Course Code: TLGS 1105 Course Title: Calculus and Linear Algebra Hall: HITL 01 & 02
Date: 19/03/2018 Duration: 2 Hours Time: 9 – 11
Instruction(s): Answer all Questions
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