Jomo Kenyatta University of Agriculture and Technology
Bsc In Mathematics and Computer Science
MATHEMATIC SC261

Spring 2016
Running head: Basics of Area and Perimeter
1
Basics of Area and Perimeter:
Name:
Institution affiliation:
Date:
Basics of Area and Perimeter
Vendors will have different amount of commodities to sale, therefore they will require
different sizes of spaces.
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Chapter 2
Square Matrices of Order 2
Abstract The main topic of this chapter is a detailed study of 2 2 matrices and
their applications, for instance to linear recursive sequences and Pells equations.
The key ingredient is the CayleyHamilton theorem, whic
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Matrix Algebra
History: (http:/wwwgroups.dcs.stand.ac.uk/~history/HistTopics/Matrices_and_determinants.
html)
The beginnings of matrices and determinants goes back to the second century BC
although traces can be seen back to the fourth century BC. Howeve
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Lecture 8
Matrices and Matrix Operations in Matlab
Matrix operations
Recall how to multiply a matrix A times a vector v:
1 2
1
1 (1) + 2 2
3
Av =
=
=
.
3 4
2
3 (1) + 4 2
5
This is a special case of matrix multiplication. To multiply two matrices, A an
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Solving Systems of Linear Equations Using Matrices
What is a Matrix?
A matrix is a compact grid or array of numbers. It can be created from a system of equations and
used to solve the system of equations. Matrices have many applications in science, engine
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
University of Nebraska  Lincoln
[email protected] of Nebraska  Lincoln
MAT Exam Expository Papers
Math in the Middle Institute Partnership
712007
The Volume of a Platonic Solid
Cindy Steinkruger
University of NebraskaLincoln
Follow this and a
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
SECTION 5.7
5.7
Volumes of Solids of Revolution
VOLUMES OF SOLIDS OF REVOLUTION
Use the Disk Method to find volumes of solids of revolution.
Use the Washer Method to find volumes of solids of revolution with holes.
Use solids of revolution to solve reall
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Name
Date
Volume of Regular Solids
All objects take up three dimensional space. Some solid objects are very regular in shape. They form triangular prisms,
rectangular prisms, cylinders, or spheres. The volume of these objects can be calculated by measuri
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Contents
8
Matrix Solution of
Equations
8.1 Solution by Cramers Rule
2
8.2 Solution by Inverse Matrix Method
13
8.3 Solution by Gauss Elimination
22
Learning outcomes
In this Workbook you will learn to apply your knowledge of matrices to solve systems of
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
prepared by itune
SPH 2173 PHYSICS FOR ENGINEERS 1 AND PHYSICS FOR TIE
A1PRECISION MEASUREMENTSObjectives:
To study some of the instruments and methods used in precision measurements , and to compute the
volume and density of various items.
Apparatus: Met
Jomo Kenyatta University of Agriculture and Technology
linear algebra
MATHEMATIC 101

Fall 2016
BIM: Cat: two SMA 2114: Applied Linear Algebra 1 Time: 1 hour
1. Define the following terms
a. A linear function
b. A basis of a vector space
c. A spanning set
2. Reduce the following system of equation to reduced row echelon form
[6 marks]
x y +2 z=1
2 x
Jomo Kenyatta University of Agriculture and Technology
linear algebra
MATHEMATIC 101

Fall 2016
SMB 0102W126016
JOMO KENYATTA UNIVERSITY
OF
AGRICULTURE AND TECHNOLOGY
UNIVERSITY EXAMINATIONS 2016/2017
EXAMINATION FOR A CERTIFICATE COURSE IN BRIDGING MATHEMATICS
DATE: DECEMBER 2016
SMB 0102: GEOMETRY
TIME: 1.5 HOURS
INSTRUCTIONS: Answer question
Jomo Kenyatta University of Agriculture and Technology
linear algebra
MATHEMATIC 101

Fall 2016
SMA 2201: LINEAR ALGERA CAT 2: TIME 1 HOUR
Define a linear function: f : R3 R 2 by f ( x , y , z )=( x , x+ y + z ) . Find
i. The kernel of f
ii. The nullity and rank of f
iii. Find the matrix representation A, of f
b) Consider the set B=cfw_ ( 1,1,1 ) ,
Jomo Kenyatta University of Agriculture and Technology
linear algebra
MATHEMATIC 101

Fall 2016
Running head: Numerical Analysis
1
Numerical Analysis:
Name:
Institutional affiliation:
SOURCES OF ERRORS IN NUMERICAL ANALYSIS
1. Input errors
The input information is rarely exact since it comes from the experiments and any
experiment
can give results o
Jomo Kenyatta University of Agriculture and Technology
linear algebra
MATHEMATIC 101

Fall 2016
Question 1
1. An error was made when creating a scatter plot for the data shown.
Identify the error.
Answer
The error made was not labelling the axes.
Question 2
Describe any clusters of data from the scatter plot.
Answer
There are two clusters of data fr
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Portfolio Manager
Profolio
Profit Percentage:
Resources:
Total Investments
VaR percentage on Stocks
VaR percentage on Real Estate
VaR percentage on Bonds
Stocks minimum holding
Real Estate minimum holding
Bond minimum holding
CD minimum holding
CD & Bonds
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Prove that if (:31, . . . , awn) and (:33, . . . 137:1) are feasible solutions to a linear program,
then so is every point on the line segment between these two points. (Note that the points
on the line segment are [053:1 + (1 o:):r:i,.,cm:n  (1 50:13:!)
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Numerical Analysis and Computation
Homework assignment 5
Show all relevant work in detail to justify your conclusions. Partial credit depends upon the work
you show.
Problem #1: Let f C (, ) and let x R be give.
(a) Prove that
Sh ,
X
f (x + h) f (x h)
= f
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Sporting Goods
Resource Requirements per Unit
(a)
Product
Basketball
Football
Rubber (lb.)
2.8
1.5
Leather (f2)
3.7
5.2
input Constraints
Total resources available
Profits ($)
600
900
Basketball
11
Football
15
Basketball
Football
Decision variables
Maximi
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
Math 128A, Spring 2016
Problem Set 04
Question 1 For equidistant points xj = j, 0 j n, n even, let
(x) = (x x0 )(x x1 ) . . . (x xn )
Use Stirlings formula to estimate the ratio (1/2)/(n/2 + 1/2) for large n.
Explain the Runge phenomenon.
Question 2 Let k
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
1) 30 pts.
Microsoft Excel Sensitivity Report (Obtained Using Standard LP/Quadratic
Engine)
Adjustable Cells
Cell
Name
Final Reduce Objective Allowable
d
Allowable
Value
Decrease
Cost
Coefficien
t
Increase
$B$4 Number to Make
Electric
30,00
0
0
55 7.00000
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
1. Do Some research (online is ok) and find your dream house or car. Youre going to include a
picture or drawing. If you put down 10% of the purchase price and finance the rest of your
purchase and pay 6.5% interest, compounded monthly for 30 years for a
Jomo Kenyatta University of Agriculture and Technology
Mechanical Engineering
MATHEMATIC EMG

Winter 2016
North Carolina State University
Department of Mathematics
Introduction to Applied Mathematics
MA 325
Assignment #2
DUE Date: March 18, 2015
A. Successful HCV treatment also called sustained virology response (SVR) is defined as a patients
viral load below
Jomo Kenyatta University of Agriculture and Technology
Bsc In Mathematics and Computer Science
MATHEMATIC SC261

Spring 2016
RESOURCES NEEDED IN ENTREPRENEURSHIP
Sources of Business Finance
The entrepreneur may obtain finance from the following main sources.
a) Debt financing
b) Equity financing
c) External and internal sources.
Debt Finance
Debt financing requires a borrowing
Jomo Kenyatta University of Agriculture and Technology
Bsc In Mathematics and Computer Science
MATHEMATIC SC261

Spring 2016
W126016
University Examinations 2014/2015
YEAR IV SEMESTER I EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN MATHEMATICS AND COMPUTER SCIENCE
SMA 2400: PARTIAL DIFFERENTIAL EQUATIONS I
DATE: JULY 2015
INSTRUCTIONS:
TIME: 2 HOURS
ANSWER QUESTION O
Jomo Kenyatta University of Agriculture and Technology
MATHEMATIC 23615

Fall 2013
CT408: Estimating the lifetime distribution function
Page 1
Chapter 8
Estimating the lifetime distribution function
Syllabus objectives
(vi)
0
Describe estimation procedures for lifetime distributions.
1.
Describe the various ways in which lifetime data
Jomo Kenyatta University of Agriculture and Technology
MATHEMATIC 23615

Fall 2013
CT407: Survival models
1.5
Page 9
The probability density function of Tx
The distribution function of Tx is Fx (t ) , by definition. We also want to know its
probability density function (pdf).
Denote this by fx (t ) , and recall that:
fx (t ) =
d
Fx (t
Jomo Kenyatta University of Agriculture and Technology
MATHEMATIC 23615

Fall 2013
CT4: Study Guide Page 31
8 Summary of useful information subject CT4
8.1 Structure of the course
_ No of Syllabus Hair 2 run 3 run
Principles ofactuarial modelling  .
_
_n
The two state Markov model
Ti1nehomogeneous Markov jump
pr
Jomo Kenyatta University of Agriculture and Technology
MATHEMATIC 23615

Fall 2013
CT405: Timehomogeneous Markov jump processes
Page 43
Definition
Vi = Waiting time of the i th life in the healthy state
Wi = Waiting time of the i th life in the sick state
Si = Number of transitions healthy sick by the ith life
Ri = Number of transitio