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-Travail-Patrie
MINISTER OF HIGHER EDUCATION MINISTERE DE L’ENSEIGNMENT
THE UNIVERSITY OF BAMENDA
UNIVERSITE DE BAMENDA
FACULTY OF SCIENCE
FACULTE DES SCIENCE
P.O. Box 39 Bambili
Tell: (+237) 22 81 63 50
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE.
SECOND SEMESTER-CONTINOUS ASSESMENT-2017/2018
COURSE CODE: MATS 2102 COURSE TITLE: Linear Algebra
Duration: 2 Hrs. Answer all questions.
I.5 Marks
Let u
o
=1 and ∀∈ℕ
∗
,
=−3
+ 2
;
=−4
+ 3
;
Find u
n
and v
n
, ∀∈ℕ
∗
II. 10 Marks
ℝ
→ℝ
Consider f:
→
2− −
−+ 2−
−− +2
sheperd of my soul ub choir
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 multiplication
4. Compute A
n
.
III. 5 Marks
1. Give the definition of symmetric and skew symmetric bilinear form.
2. Show that any bilinear form is a linear combination of a unique skew bilinear form.
3. Prove that if f=ExE→ℝ
is a skew bilinear form, then f(x,x)=0 for all x∈.
IV. 10 Marks
Solve the following system
⎩
⎪
⎨
⎪
⎧
#$
#%
=2− 2 −
#$
#%
=+ 5−
#$
#%
=2+ 4 +
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