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Solution
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MAT 1348B (Prof. P. Scott) Homework 6
Due Thursday, March 10, 2016 by 11:00 AM
Instructions:
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Lecture 2: Vector Spaces
1
What is a Vector
Usually define as a geometric object that has both magnitude and direction.
What is the polar representation of the complex number z=-3?
z=-3
z=3
you may say z = 3ei0 , but that would be wrong, because you the d
Quiz 1
May 9, 2016
Q1) The number 2i is
A Real Number
B Pure Imaginary
C Complex Number
D Pure Imaginary and Complex
E Pure Imaginary and Real Number
Q2) Let x be any imaginary number and y be any real number. Which of
the following is correct
A x2 0 and
1. Suppose X is a subspace of R6, that X 75 cfw_O and that X 75 R6. Which of the following
statements are true?
I. X has a spanning set consisting of 6 vectors.
II. X has a linearly independent subset consisting of 6 vectors.
III. 1 S dimX S 5.
IV. X has
Lecture 19
Determinants
1
Determinants: Algebraic Definition
Algebraically determinant of a square matrix A (denoted as det(A) is defined
to be:
For a 1 1 matrix A = [a],
det(A) = a.
a b
For a 2 2 matrix A =
c d
det(A) = ad bc.
a11 a12 a13
For a 3 3 ma
Quiz 4
June 6, 2016
Q1) Let V be a vector space under the operations , and let
cfw_v1 , v2 , , vm V. Which of the following is true?
A The set cfw_v1 , v2 , , vm is linearly independent if and only if the
only solution to
(1 v1 ) (2 v2 ) (m vm ) = 0
is
Let W = cfw_(x, y, z) R3 | 5x 4y + z = 0 is a subspace of R3 .
1. Find a basis for W.
2. Show that cfw_(1, 0, 5), (10, 13, 2) is a orthogonal basis of W.
3. Let v = (4, 5, 0) R3 , find the orthogonal projection of v onto the
subspace W.
Basis of W : we h
Lecture 21
Eigenvalues and Eigenvectors of a (square)
matrix
1
Eigenvalues, Eigenvectors and EigenSpace
Let A be an n n matrix. A number R is called an eigenvalue of A if
there exists a non-zero vector x Rn . such that
Ax = x.
The non-zero vector of x is
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MAT 1348B (Prof. P. Scott) Homework 5
Due Thursday, March 3, 2016 by 11:00 AM (new due time !)
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MAT 1348B (Prof. P. Scott) Seventh Homework Assignment
Due Thursday Mar. 17, 2016 by 11:00am
Instructions:
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ANNETT
Student number:
MAT 1348B (Prof. P. Scott) First Homework Assignment
Due Wednesday, Jan. 20, 2016 by 3:00pm
Instructions:
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Lecture 3
1
Lines and Planes
Line Segment and Line
Shortest distance between two given points is called a line segment.
Extending a line segment in both direction infinitely gives you a line
1
1.1
1
Parametric Equation of a Line in R2 and R3
Suppose we ar
Lecture 23
Linear transformations
Definition
Let U and V be vector spaces. A function T : U V is called a linear
transformation if it satisfies the following two axioms.
For all u, u0 U,
T (u + u0 ) = T (u) + T (u0 ).
For all u U and for all r R,
T (ru)
LECTURE 12
n
A set of all points in |R that satisfy all the equations
REDUCED ROW ECHELON FORM (RREF):
In addition to the property 1,2 and 3 of row echelon form (REF)
4 Each leading 1 is the only non-zero entry in its column.
MAT 1341 3X Final, 2016
October 03, 2016
Instructor: Raza Ali Kazmi
Last Name:
1
F
2
E
3
F
4
B
5
C
6
F
7
E
8
F
9
E
10
E
sub-total
11
12
13
14
Total
First Name:
Student Number:
Seat Number:
PLEASE READ THESE INSTRUCTIONS CAREFULLY.
1. You have 3 hours
Lecture 18
Matrix Inverses
1
Invertible Functions
In lecture 4 we define a function. Let X and Y be two sets. A function f from
X to Y is a rule that takes every element from X and map to Y, such that
if f (x) = y1 and f (x) = y2 for x X and y1 , y2 Y, we
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MAT 2348 Second Homework Assignment
Due Thursday, Feb. 6, 2014 at 11:20am
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a draft. You may write on both sides of the paper or inser
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MAT 2348 First Homework Assignment
Due Thursday, Jan. 23, 2014 at 11:20am
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MAT 2348 Third Homework Assignment
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MAT 2348 Fourth Homework Assignment
Due Thursday, Mar. 20, 2014 at 11:20am
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a draft. You may write on both sides of the paper or ins
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MAT 2348 Fifth Homework Assignment
Due Thursday, April 3, 2014 at 11:20am
Instructions: Show all relevant work to receive full credit. Submit a nished product, not
a draft. You may write on both sides of the paper or inse
Graphs for MAT 1348
Graphs for MAT 1348
1 Intmductian
1.1 m Graphs
Denitiom 1.1 is am: , Where
V is a nonempty set of g i: - Vfk
and E isasetof 2d%'-$ _:> f .u?".
together with a function £
(called the incidence function, as
MAT 1348 The Most Important Concepts and Questions
Logic and Proofs
Concepts
proposition
logical connectives, compound proposition
logical equivalence
tautology, contradiction, contingency
disjunctive normal form
truth tree
rules of inference, arg