CHAPTER 6. MATRIX ALGEBRA
6.4
44
Solving Systems by Reducing Matrices
Example 6.4.1. The admission fee at a small fair is $1.50 for children and
$4.00 for adults. On a certain day, 2200 people enter the fair and $5,050 is
collected. How many children and
February 12, 2014
12:27 AM
New Section 1 Page 1
Printout
February 10, 2014
8:21 AM
New Section 1 Page 2
Page 2
February 10, 2014
8:21 AM
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Page 3
February 10, 2014
8:21 AM
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February 10, 2014
8:21 AM
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February 3/5/7, Math 1115, Lecture #11/#12/#13
Section 7.3: Multiple optimum solutions
When an objective function attains its optimum value at more than
one feasible point, we say that multiple optimum solutions exist.
Example 36 Minimize
Z = 6x + 14y
sub
Math 1115, March 17, Lecture #25
Assignment #7 due Wednesday March 19
Final exam is April 14 at 8:30am in Dalplex
(Need to bring Student ID Card for attendance)
Finishing up from last Class:
March 17-28 (approximately), Math 1115,
Chapter 11
Differentiati
February 24/26/28/March 3, Math 1115,
Lecture #16/#17/#18/#19
8.38.7
Denition 19 A sample space S for an experiment is the set of all
possible outcomes of the experiment. The elements of S are called
sample points. If there is a nite number of sample poin
March 1014, Math 1115,
Lecture #22 24
10.1-10.3
Limits
f (x) =
x3 8
.
x 2
Denition 27:
The limit of f (x) as x approaches a is the number L, written
This means as x gets very close to a (from the left and right) then
y = f (x) gets very close to L. If no
The rst midterm will be in class on January 31. It will be multiple choice. No
calculators are allowed and you will be provided with a formula sheet. The midterm
will cover Chapter 5, Chapter 6, and Section 7.1 (the material on the rst three
assignments).
Math 1115 Course Notes
These notes were originally created by Dr. Rob Noble when he taught the course.
I have modied them slightly and will continue to do so throughout the semester.
February 28, 2014
These notes are based closely on the text book for thi
Math 1115 Course Notes
These notes were originally created by Dr. Rob Noble when he taught the course.
I have modied them slightly and will continue to do so throughout the semester.
April 1, 2014
These notes are based closely on the text book for this cl
Math 1115, March 17, Lecture #25
Assignment #7 due Wednesday March 19
Final exam is April 14 at 8:30am in Dalplex
(Need to bring Student ID Card for attendance)
Finishing up from last Class:
March 17-28 (approximately), Math 1115,
Chapter 11
Differentiati
January 27/29, Math 1115, Lecture #9/#10
Section 7.2: Linear Programming
Denition 12: A linear function in x and y is a function P of the form
P = P(x, y ) = ax + by
for constants a and b.
A linear programming problem is one where we wish to optimize
(max
January 22, Math 1115, Lecture #8
Section 6.5 Continued . . .
Denition 10: The system AX = B is called homogeneous if B is
equal to the zero column vector. Otherwise, the system is
nonhomogeneous.
Example 29:
a)
2x + 3y = 4
3x 5y = 0
b)
2x + 3y = 0
3x 5y
February 10/12/14, Math 1115,
Lecture #14/#15/#16
Chapter 8: Introduction to Probability and Statistics
Math 1115 Midterm #2 is March 7: Suppose the test has 8 questions
and for each question there is 5 options to choose from. What is the
probability of g
March 17-28 (approximately), Math 1115,
Chapter 11
Differentiation
Denition: The derivative of a function f is the function f
(read f prime") dened by
provided that this limit exists. If f (a) exists for a given value a, f is
said to be differentiable at
Math 1115, March 10, Lecture #22
-Pick up Midterm 2 (and Midterm 1) in my ofce during ofce
hours (MWF) 2:45-3:45
-Check that grade on Midterm 2 (and Midterm 1) paper is same
as what is recorded on Bblearn
-Assignment #7 is due March 17
-Final Exam is Apri
Math 1115 Lecture #16, Feb. 24
February 24/26/28/March 3, Math 1115,
Lecture #16/#17/#18/#19
8.38.7
Denition 19 A sample space S for an experiment is the set of all
possible outcomes of the experiment. The elements of S are called
sample points. If there
January 10, Math 1115, Lecture #3
Section 5.3: Interest Compounded Continuously
More interest is earned the more it is compounded.
Earn increasingly more interest by compounding
weekly, daily, per hour, per minute, per second etc
Proposition 4
The formula
January 13, Math 1115, Lecture #4
Section 5.5: Amortization of Loans
A loan is said to be amortized when part of each
payment is used to pay interest and the remaining
part is used to reduce the outstanding principal.
Monthly payment R=?
Present Value: A=
January 17, Math 1115, Lecture #6
Finishing off Section 6.3 . . .
Denition 7: The n n identity matrix, denoted by In , is the square
matrix whose main diagonal entries are all 1s and all other entries
are 0. For example:
I2 =
, I3 =
Matrix Equations Matri
January 15, Math 1115, Lecture #5
Section 6.2 continued
Scalar multiplication
Denition 5: If A is a matrix and k is a real number (scalar), then the
matrix kA is the matrix obtained by multiplying every element of A by
k.
1 3
2 3
Example 18 Let A =
and B
January 20, Math 1115, Lecture #7
Section 6.4 Continued . . .
Recap from Last time: A matrix is said to be a reduced matrix
provided that all of the following are true:
1. All zero rows are at the bottom of the matrix.
2. For each nonzero row, the leading
Math 1115 Mathematics for Commerce Exam
Chris Levy
April 14, 2014
First name(s):
Last name:
Signature:
Student number:B00
No calculators or handheld devices are allowed during the midterm.
You should only have writing utensils out during the midterm.
A fo
n
n
S = P (1 + r)
re =
P = S(1 + r)n
re = ei 1
1 (1 + r)n
an r =
r
A = Ran r
1. Periodic payment: R =
sn r
i
1
1+
n
S = P ert
P = Sert
(1 + r)n 1
=
r
S = Rsn r
A
an r
2. Principal outstanding at beginning of kth period: Rank+1 r
3. Interest in kth payment
CHAPTER 11. DIFFERENTIATION
11.5
97
The Chain Rule
Given functions f and g, the composition of f and g, denoted f
(f
g, is given by
g)(x) = f (g(x).
Computing the value of the composite function f g at x is a two-step process:
we first substitute x into g
Chapter 8
Introduction to Probability
and Statistics
8.1
Basic Counting Principle and Permuations
Example 8.1.1. Jessie has 5 tops, 3 pairs of pants, and 2 pairs of shoes. In
how many ways can she get dressed?
Solution: We can systematically list her opti
CHAPTER 5. MATHEMATICS OF FINANCE
5.4
20
Annuities
An annuity is a finite sequence of payments made at fixed periods of time over a
given interval. We consider periods of time that are always of equal length, and
this length is called the payment period.