Calculus and Linear Algebra (GSDR2107)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 200
Year: 2018
The University of Bamenda Université de Bamenda
Higher Institute of Transport Institut Supérieur de
And logistics Transport et Logistique
Department of Basic Sciences
CA1 Academic Year : 2017/2018
Course Code: TLGS 1107 Calculus and Linear Algebra Duration: 3 hours
Lecturer: Dr. Emmanuel Fouotsa
1. Consider the following matrices :
A =
2 −3 −1
−4 5 −2
3 −4 3
B =3
5 −2 −1
3 −1 4
C=
3 5
−2 4
−4 2
(a) For each of the following operations, identify the possible operations and explain why other operations are not
(no computation is required). 3B−46
T
, BA, AB, BC, CB, A
3
, A C.C +2
(b) Find the third row of AO
(c) Find the second column of AC.
(d) Find the transpose of C 2. Consider the following matrix
A =
4 −3 5
2 7 −3
6 1 2
Write A as die sum of a symmetric matrix and a skew-symmetric matrix V.
2. We consider the matrix
A =
7 1 −1
−11 −3 2
18 2 −1
(a) Find the (2,3) cofactor of A
(b) Compute the determinant, det(A), of A.
(c) Is the matrix A invertible? Justify your answer.
(d) Compute A
3
(e) Show that. A
3
− 12A — 16I
3
=. 0 where 0 represent the zero square matrix of order 3.
4 Consider the complex numbers Z
1
= 1 - i
√
3,
−1+
(a) Find the modulus and the principal argument of each of these complex numbers
(b) write Z
1
and Z
2
in the exponential form
(c) Compute
(d) Find the modulus and the principal argument of the complex Z
3 =
Z
1
. Z
2
(e) Find the exact value of
and sin
. (Hint: you may write ZyZ
2
in the algebraic form)
5. Are the vectors u(1, 2,
√
7) and v ( -
√
7 0. 1) orthogonal? Justify your answer.
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