MAT-703
SUMMARY NOTE ON COMPLEX NUMBERS
T. Zakon
An overview of the evolution of number systems
Starting with counting numbers, our number system evolved gradually for a variety of purposes, both
comp
MAT- 703
Summary Note on Subspaces, Spans, Basis, Dimension
T. Zakon
CONCEPTS AND DEFINITIONS
v1 , v2 , vm is a vector of the form w = c1v1 + c2 v2 + + cm vm where
the ci are scalars ; in other word
MAT-703
T. Zakon
STUDY GUIDE FOR TEST I
September, 2016
Note: You should expect test questions to involve definitions, interpretation and comprehension, some
proofs, as well as questions involving com
MAT-703
STUDY GUIDE FOR TEST II
October, 2016
T. Zakon
Complex Numbers
Definitions (be able to state):
What is a complex number? What are the real part and imaginary part
of a complex number? What is
MAT-703
T. Zakon
ASSIGNMENT 3
Complex Arithmetic
REFERENCES: TEXTBOOK PP 234 249; Summary note on Complex Numbers (to be posted on
Omnivox)
HAND IN questions 3(h), (i), 4, 5(b), 6, 7(a), (b), 8(a), (b
MAT- 703
Assignment 4
T. Zakon
Subspaces, basis and dimension
See posted Summary Document on Subspaces. It includes definitions and outline of procedures relevant to the
problems below. You may use th
201-NYC-05 Fall 2016
Homework
M. Hamel
August 17, 2016
Homework: Homework will be assigned weekly. There will be three types of homework assigned:
WeBWorK, written and collected assignments, and sugge
MAT NYC
ASSIGNMENT 3
1. A square (n x n) matrix P is called idempotent if P 2 P. (For example the zero matrix On
and the identity matrix I n are idempotent.) Show that:
1 1 1 0
1 1 1
a)
and
are idem
MAT NYC
Linear Algebra
Solutions
Course Package
Jean-Francois Deslandes
Marianopolis College
Fall 2015
Section 1
Vector algebra
Problem 1.1
Consider the vectors, , and , shown below.
u v
w
Find the gr
Section 1
Vector algebra
Problem 1
The structure of a methane (CH4) molecule is such that the carbon atom is positioned at the
center of the four hydrogen atoms. The four hydrogen atoms are at positi
MAT NYC
Linear Algebra
Course Package
Jean-Francois Deslandes
Marianopolis College
Fall 2015
2
Differential Calculus
Mat NYC
Fall 2015
Instructor
Office
E-mail
Phone
Jean-Francois Deslandes
I-322
j.de
Section 3
Linear systems and Gaussian elimination
Problem 1
Using Gaussian elimination, reduce the following system to its echelon form. Identify all free and
leading variables and write its general s
Section 4
Matrix algebra
Problem 1
Using index notation, demonstrate the left-distributivity property:
C(A+ B) = CA + CB.
Demonstration done in notes
Problem 2
1
1
2
6
A quadrilateral has its vert
Section 6
Vector spaces and subspaces
Problem 1
Define the following concepts :
a)
b)
c)
d)
S is a subspace
The subspace S = spancfw_ u , v , w
Linear independence of vectors u , v , w .
The vec
Section 5
Determinants and its applications
Problem 1
2
4
1
A 3 1 13
Consider the matrix
4
1
k2
Compute the determinant of A. What values of k will lead to 1 solution, no solution or infinitely
man
Section 2
Lines and planes
Problem 1
Consider the plane whose equation is 2 x 3 y 6 z 12 . Find a unit vector that is normal to the
plane.
Solution
2 3 6
, ,
7 7 7
Problem 2
The vertices of a triang
201 NYC
Homework 3
Problem 1.16
Let
u 3 b 2 a
, where and are perpendicular vectors.
a
b
c) Find the length of the vector
Problem 1.17
Let us assume that
u
and
v
;
a u
are unit vectors that are separa
201 NYC
Homework 2
Problem 1.13
Consider the triangle show below. Use a projection to find the coordinates of point N if it is the point on
the segment AB that is nearest to point C.
Problem 1.15
Dete
201 NYC
Homework 1
Problem *
Consider a triangle whose vertices are
and
C
. Assume that
Q
of the distance between
segment
that
P
,
A B
,
is the point that is 2/3
A
and the midpoint of
BC . In the same
MAT-NYC
Lab 4: Polar Form of Complex Numbers
1. Convert the following numbers to rectangular form.
a) 3 cos 4 + i sin 4
b) 5 cis
c) cos 7 + i sin 7
3
3
2
4
4
d) 10 cis 248 (give two decimal places)
2
MAT-NYC
Lab 5: Lines & Planes in R3
1. True or false? (Note: distinct in this context means not coincident)
a) Two distinct planes perpendicular to a given line are parallel to each other.
b) A plane
201-NYC E
1.
Assignment 4
a) A triangle is formed by joining two adjacent corners at the
bottom of a cube to the midpoint of the edge at the top of
the opposite face, as in the picture on the right. U
Course 2
August 27, 2015
8:20 AM
Nature vs Nurture
Answer might have a big impact on social policy
Where is if worth intervening to help kids and families?
Burt sometimes it is hard to know!
Child
201-NYC
Exercises on (R)REF, rank
1. Decide if each of the following matrices is in RREF, REF (bot not RREF), or neither REF nor
RREF.
1 4 3 0
1 0
a) 0 0
0 0
0 1
b)
0 1 1 7 0 0
9 0 0
d) 0 0 1
0 0 0
201-NYC
Exercises on Number of Solutions
1. Give the general solution to the linear system whose augmented matrix has been reduced to the
following. Give the solution in (i) parametric equation form,
201-NYC
Exercises on Elimination
1. Solve the following systems of linear equations by Gaussian elimination with back-substitution.
x1
2x2 4x3 + 13x4 = 11
3x1 +
8x2 + 16x3 49x4 = 45
2x2 3x3 + 14x4 =
Christopher Turner
Marianopolis College
201-NYC-05 (Linear Algebra I); A15
Addendum to Course Outline: Evaluation Method
Your evaluation in this course will comprise a series of assignments, two tests
COURSE OUTLINE
Linear Algebra I
TERM:
PONDERATION:
DISCIPLINE:
COURSE CREDIT:
PREREQUISITE:
OFFICE HOURS:
Autumn 2015
3-2-3 (class-lab-homework)
Mathematics
2 2/3
Sec. V Math TS or Sec. V
Math SN or e