MA122 Mock Midterm
Name:
Time Allowed: 80 minutes
Total Value: 65 marks
Number of Pages: 6
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while comp
To the linear system
311X1 + 312X2
a21X1 322X2
aml X1 + 3m2X2
we associate two matrices:
coeffICIent matrix
all 312 31m
321 322 32:1
3ml 3:112 3min
+ £31an : b1
+ £39an : b2
+ 3111an : bm
a ugm
Clicker Question 1 (Sept. 17)
Which one 13 a, vector equation for the line through the point P(1, 1) with
. . > 1
threat-1011 vector (1 : _1 E §1-2i
Addition:
Definition (Rn)
X1 +y1
Xn+Yn
Scala
MA122 Mock Midterm
Answers
(Full Solutions will NOT be posted;
use the MAC drop-in help centre if you have any questions.)
s
* Please remember that the mock test was meant as a means of providing an e
Definition (Dot Product)
The dot product of vectors 2' = f , )7 = f in R is Theorem
Let if}? E R and t E R. Then
0 2-220, and 2.2:0 ifand only ir2:6,
a)? i7:i7-i<:
e 2* 0742):)? in)? z,
o (rm-n)? Wm
3.2 Linear Mappings
1
2
A function that satisfies (L1) is said to preserve addition.
A function that satisfies (L2) is said to preserve scalar multiplication.
A function that satisfies both properties
Fall Term, 2015
MA122A, B & C Introductory Linear Algebra
Instructor: Dr. Ping Zhang (Sections A & C)
Office: BA303D (Bricker Academic Building) Telephone: ext. 2972 E-mail: [email protected]
Office Hours
MA122 Mock Midterm
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the midterm based solely
Directed Line Segments
We denote the directed line segment from P to Q by Pﬁ .
If 53 (j are the vectors corresponding to the points Pg Q (respectively), then
172
—r
Po:a—e
O XI
we may wish to treat
Clicker Question 1 (Eloy. 20)
In which pair of vectors below. the two vectors are NOT orthogonal?
1 0 1 4
U —3 2 —3
A' 3 0 B' 3 2
{J —1 4 —1
0 1
0 —1 {a 4;, EN? 1}
o. _ D. :1: y 61113 —=—
0 1 HW‘H?”
Applications to Euclidean vector spaces
Lemma
A set of vectors {i71. . . . . W} in R” is linearly independent if and only if the
rank of the coefficient matrix of the homogeneous system
t1l71+'“+tk\
Clicker QLIEStiOIl 1 (NIay. 13)
Which 0118 is NOT a subspace of R3?
331 £131 1 3 4
A. $2 332 :151 2 +tg 2 T {515152,t3 ER
333 $3
I$1=$2=$3€R:$120:$23>0-333>0}
H ]
0H2] [:ngHW}
{[1 Theorem
Let ‘31,. .
1‘
If "' -'o ‘éé'1.r‘"'$ so *1: t- s. e:-
A vector v 111 R” 1s unlquelv determined bv1ts norn1 v and the amt vector
in its direction 6. In other ivorda given a direction and a real number 1“ Z 01
.
Clicker (211135131011
1
The cross product of the vectors ? : [ 2
1
3 —3
A. 0 B. 0 C. 0 2.1 Systems of Linear Equations
DEFINITION
An equation in a variables (unknowns) in, . . . , I” that can be writt
MA122A Introductory Linear Algebra
Spring Term, 2014
Instructor: Dr. Ping Zhang
Office Hours: Tuesdays & Thursdays 2:00 -3:00 p.m. (or other times by appointment)
Communication:
* All important course
§1.4 Projections The Perpendicular Part
For any vectors f, )7 E R, with a? at 6, dene the projection of )7 perpendicular to J?
to be
136er? 5 = )7 - ijz 37
perpj-(y) is perpendicular to f, and p11)
That is:
3:
(Expansion needs to be indicated by an arrow)
The arrow Technique is a
Example:
=
ij
ij
This matrix is called the
= (cof A)
or the cofactor matrix of A
(adjugate matrix)
= (cof A)
T
Let A
MA122 Mock Final Exam
Name:
Time Allowed: 150 minutes
Total Value: 100 marks
Number of Pages: 8
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while
MA122 Mock Midterm
Name:
Time Allowed: 80 minutes
Total Value: 65 marks
Number of Pages: 6
Instructions:
Non-programmable, non-graphing calculators are permitted. No other aids allowed.
Answer in the
§3.4
Theorem/Definition Let A be an m x n matrix. The set
S:{)_<R | Af:5}
of all solutions to a homogeneous system A)? : 5 is a subspace of R. It is
called the solution space of the system.
Definiti
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MA122
ock Final Exam
Time Allob ed: 1,lh11in11t( s
Total Value: 100!narks
Number of Pages: b
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