UNIVERSITY OF ZIMBABWE
HASTS114
HACS113
HFM113
HDSCS116
BSc Honours in Mathematics Level 2
LINEAR MATHEMATICS AND ORDINARY DIFFERENTIAL EQUATIONS
July 2022
Time : 2 hours
Candidates may attempt a total of FIVE questions, at MOST TWO questions from each
section.
SECTION A
A1. Determine whether the vector y=
−5
3
0
is a linear combination of the vectors
y1=
−1
2
1
,y2=
3
1
2
,y3=
1
5
4
,y4=
−6
5
1
. [10]
A2.
Use determinants/row reduction to solve the following system of linear equations
2x1+x2+ 7x3−2x4= 4
3x1−2x2+ 11x4= 13
x1+x2+ 5x3−3x4= 1.
[10]
A3. (a) Find all solutions to the following system of linear equations
2x1−3x2+x3+ 7x4= 14
2x1+ 8x2−4x3+ 5x4=−1
x1+ 3x2−3x3= 4
−5x1+ 2x2+ 3x3+ 4x4=−19.
[10]
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