Introduction to Linear Algebra
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MATH1014: Introduction to Linear Algebra
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any area of your assignment. The School of Mathematics and Statistics encourages
some collaboration between students when working on problems, but students must
write up and submit their own version of the solutions.
This assignment is worth 10% of your final assessment for this course. Your answers should be
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Assignment Questions:
1. Consider the vector n =
3−1
2
and the points A = (1,−1, 3) and B = (1, 3, 5) in R3.
(a) Give the parametric vector equation of the straight line L through A and B.
(b) Give the Cartesian equation of the plane P through A, which n is normal to.
(c) Does the line L lie in the plane P? Justify your answer.
2. Consider the lines L1 and L2 in R3 given by the parametric equations
L1 :
xy
z
=
57
−2
+ t
25
−3
, t ∈ R,
L2 :
xy
z
=
8−13
−9
+ s
1−3
−2
, s ∈ R.
Determine whether L1 and L2 intersect and find the intersection point if they do.
3. Let c =
[
4
3
]
and a =
[
2
1
]
be two 5-ary vectors. Find all 5-ary vectors v =
[
x
y
]
(i.e., the
vectors v whose components x and y belong to Z5) such that
c · (v− a) = 0 (mod 5).