Linear Algebra 1 (MATS2202)
Mathematics and Computer Science - MCS
Semester: Second Semester
Level: 200
Year: 2018
REPUBLIC OF CAMEROON REPUBLIQUE DU CAMEROUN
Peace-Work-Fatherland Paix-Travaille-Patrie
MINISTRY OF HIGHER MINISTERE DE L’ENSEIGNEMENT
EDUCATION superieure
THE UNIVERSITY OF BAMENDA UNIVERSITE DE BAMENDA
P.O. Box 39 BAMBILI
TEL: (+23)22 81 63 50
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
SECOND SEMESTER —CONTINIOUS ASSESMENT-2017/201S
COURSE CODE: MATS 2102 COURSE TITLE: Linear Algebra
DURATION: 2 HRS Answer all questions.
I. 5Marks.
Let u
0
= 2, v
0
= 1 and ∀n ∈ ℕ*,
=−3
+ 2
;
=−4
+ 3
;
Find
and
, ∀n ∈ ℕ*,
II. 10 Marks.
ℝ
→ℝ
Consider f :
↦
2− −
−+ 2−
−− + 2
1.
Find the matrix A representing f.
2.
Find the kernel of f and the image of f.
3.
Compute the eigen values of f and the corresponding eigen vectors together with the multiplicities
4.
Compute A
n
.
III. 5 Marks.
1. Give the definition of symetric and skew symetric bilinear form.
2. Show that any bilinear form is a linear combination of a unique symetric bilinear form and a unique
skew bilinear form.
3. Prove that if f : E x E →ℝ is a skew symetric bilinear form, then f ( x , x ) = 0 for all x ∈ E .
IV. l0 Marks
Solve the following system
⎩
⎪
⎨
⎪
⎧
!"
!#
=2−2 −
!#
!$
=+ 5−
!&
!$
=2+4 +
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