The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
11.
Longer Solutions to Selected Exercises for Week 8
2016
The matrix equation A0 = 0A = 0 makes sense by interpreting the symbol 0 as an
abbreviation for zero matrices of compatible d
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Exercises for Week 1
2016
There are thirteen teaching weeks. There will be one set of exercises each week from Week 1
through 12, except for Weeks 5 and 11, when quizzes will be held d
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Exercises for Week 2
2016
Preparatory exercises should be attempted before coming to the tutorial. Questions labelled with
an asterisk are suitable for students aiming for a credit or
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Exercises for Week 8
2016
Preparatory exercises should be attempted before coming to the tutorial. Questions labelled with
an asterisk are suitable for students aiming for a credit or
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
7.
Longer Solutions to Selected Exercises for Week 3
2016
(i) First observe that QP = 2i + 2j + k and QR = i + 2j + 2k , yielding
QP QR = 2 + 4 + 2 = 8 > 0 ,
so that P QR is acute (n
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
9.
Longer Solutions to Selected Exercises for Week 2
2016
(ii) Observe that P Q = SR = 2i 2j k so P QRS is a parallelogram. But
|P Q| = |P S| = 3 ,
so P QRS is a rhombus. This rhombu
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
8.
If |v| = 2, find |u| in each of the following cases.
(i)
9.
u = 3v
(ii) u = 21 v
(iii) u = 3v
(iv) v = 3u
In each diagram below, find the unknown vector in terms of a and b.
?
b
a
1
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Longer Solutions to Selected Exercises for Week 1
11.
2016
6
8
d
By Pythagoras d = 82 + 62 = 10 . If is the angle to the horizontal then cos =
6/10 , yielding an angle 53 . Thus the re
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Exercises for Week 3
2016
Preparatory exercises should be attempted before coming to the tutorial. Questions labelled with
an asterisk are suitable for students aiming for a credit or
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
7.
Board Tutorial for Week 3
2016
Consider the following points in space:
P (1, 1, 1) , Q(1, 1, 0) , R(0, 1, 2) , S(2, 3, 3)
(i) Recall from an earlier exercise that P QRS is a rhombus
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
6.
2016
Board Tutorial for Week 2
Given points A(4, 1, 5) and B(6, 1, 2) in space, find
(i) the position vectors of A and B in terms of i, j and k;
(ii) the displacement vector AB in t
practice
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The University of Sydney
School of Mathematics
& Statistics
MATH1902 Practice for Quiz 1.
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The real quiz (15 questions) lasts 40 minutes and tests material
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