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LIA502S- LINEAR ALGEBRA 1 - JAN 2020 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BAMS
LEVEL: 5
COURSE CODE: LIA502S
COURSE NAME: LINEAR ALGEBRA 1
SESSION: JANUARY 2020
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 84
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINERS
DR IKO AJIBOLA
MODERATOR:
MR BENSON OBABUEKI
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 4 PAGE (including this front page)
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QUESTION 1 (16 marks)
1.1 If w=2i-3j7+k, v=3i+ j-2k, w=i+5j+3k are vectorsin R’, find
1.1.1 U+tv.
[3]
1.1.2 2u -3+v4w
[4]
1.2 Suppose w=(1,-2,3) and v=(2,4,5) Find:
1.2.1 cos0,where @ is the angle between u and v;
[2]
1.2.2 proj(u,v), the projection of u unto v
[3]
1.2.3 d(u,v), the distance between u and v
QUESTION 2 (25 marks)
2.1 Rewrite the following linear system in standard form.
2x+4z+1=0
2z+2w-2=x
—2x—z+3w=-3
[2]
yt+zt+t=wt+4
Find:
2.1.1 The coefficient matrix.
[2]
2.1.2 The vector of constants
[2]
2.1.3 The augmented matrix.
[2]
2.1.4 The associated homogeneous system
[2]
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2.2
Determine whether the vector
0
-|
2
1
U=|2] is alinear combination of v,=| 1 |, v,=| 9], v; =| 1
[10]
1
0
]
1
2-31 5487
2.3 If D=| -4 3-7i| Find D” the Hermitian matrix of D.
[5]
-6-i
Si
QUESTION 3 (17 marks)
3.1
Write the vector V=(1,-2,5) as a linear combination of the vectors
uy =(I,1,1), u, =(1,2,3),
Uu; =(2,-1,1).
[12]
x
3.2 Show that V=<|y|,x,yeR> isasubspaceof R’.
[5]
0
UESTION 4(16 marks
4.1
List out the four essential steps you will use in finding the inverse of a 3X3
Matrix A.
[4]
2 -l1 3
4.2
Using the steps listed in (4.1) obtain the inverse of d=|1 -—2 1
[12]
0 -1l 2
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QUESTION 5 (10 marks)
Use appropriate definition to investigate whether the polynomials
p,(t)=2 +3t+4, p,(t)=" -3¢, p,(t)=4t—-5 are linearly dependent or
8
linearly independent.
END OF EXAMINATION