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LIA502S - LINEAR ALGEBRA 1 - 1ST OPP - NOV 2022 |
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nAml BIA UnlVERSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of Science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BSAM
LEVEL:
5
COURSE CODE:
LIA502S
COURSE CODE: LINEAR ALGEBRA 1
SESSION:
NOVEMBER 2022 PAPER:
THEORY
DURATION:
3 HOURS
MARKS:
100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER:
MR. GS MBOKOMA, DR. N CHERE
MODERATOR:
DR. DSI IIYAMBO
INSTRUCTIONS
1. Attempt 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 black or blue inked, and sketches must be done in
pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 2 PAGES (Including this front page)
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Question 1
1.1 Let u = 2i + 2j + 3k and v = -i + j + 4k.
a) Find the unit vector ii in the direction of u.
[4]
b) Find the projection vector of u onto v.
[6]
b) Find the angle (in degrees) between u and v. Give you answer correct to 2 d.p. [7]
1.2 Determine the area of parallelogram whose adjacents sides are a = 2i - 4j + 5k and b =
i - 2j - 3k. Leave your answer in surd form.
[5]
1.3 If A and B are vectors, then show that (A - B) x (A+ B) = 2(A x B)
[5]
Question 2
2.1 Let A be a square matrix and let
a) Find S+P.
[3]
b) Show that S is symmetric and P is skew-symmetric.
[6]
c) If A is symmetric, then show that S = A and P = 0.
[4]
1
2.2 Conside, the m,t,ix A (
~5 ) .
a) Use the Co.factor expa.ns-ion method. a.long the second cul·urnn to evaluate the cletenui-
nant of A.
[7]
b) Is A invertible? If it is, Use the Gauss-Jordan Elimination method to find A- 1 . [14]
c) Find det (3(2A)- 1).
[6]
Question 3
Determine whether or not the vector (-1,1,5) is a linear combination of the vectors (1,2,3), (0,1,4)
and (2,3,6).
[15]
Question 4
Let W= {(x,y,z) E~ 3[3y+2z=0}.
a) Verify that W is a subspace of ~ 3 .
[12]
b) Find a basis for W.
[6]
1