math project

EAST LA COLLEGE

DEPARTMENT OF MATHEMATICS

MATH 270 (LINEAR ALGEBRA)

MINI PROJECT 3

SPRING SEMESTER 2020

INSTRUCTIONS — PLEASE READ!!

In this mini project, you are expected to provide a “typed cover sheet” of font size 12 using

“Times New Roman”, containing the course name, project number, your name, date and

your professor’s name using the correct title. The remaining pages must be labeled with the

following three components :

(1) Problem Statement (Must be typed)

(2) Background Information (Must be typed)

(3) Required Work & Solution (Hand-written or typed)

The “Problem Statement” is the given problem provided on the second page, which must be

typed by you rather than performing “cut and paste” from this pdf file.

The “Background Information”, should not focused on the given mini-project problem but it

should be more generalized and applicable to any problem, using your own words. Moreover,

it should explain the method used in solving the problem in a broad perspective and steps

needed to obtain a solution. So it should help someone learning this approach for the first

time, have a basic understanding of the steps needed to solve any problem of that particular

type.

The “Required Work & Solution” must contain all the necessary algebra work (written

neatly and easy to follow) in finding the solution. This mini-project is a representation of

your work and no one else.

This project is worth 30 points and must be submitted electronically to your professor using

Canvas email or ELAC email(carterdm@elac.edu), on or before 9:00am on May 28, 2020.

Late submission will not be accepted and receive a grade of 0%. You must submit your mini

project as one pdf file. Once you have electronically submitted your mini-project then your

professor will send you a confirmation email of that receipt within 12 hours. If you don’t

receive a reply from your professor then this means your email was not received and your

advised to submit it using the alternative email (ELAC email or Canvas email).

Moreover, if any background information or required work for the solution is viewed as

similar or identical, then the respective students will receive a 0%, which is considered

cheating. Also copying any work online for the solution is also classified as cheating and

won’t be tolerated. You are allowed to work together but a copy of another student’s work

or online work is not permitted. Your professor isn’t allowed to offer any assistance in this

mini-project nor check your unfinished mini project. Additionally, points will be deducted

for any messy work displaying scratch marks, and the like, or work that isn’t legible (such

as small script) or misspelled words or submission of your mini-project using a file that isn’t

classified as a pdf file or submitting more than one file.

Below you will find the problem for this mini project. Good luck !

Mini-Project 3

Let A be the n × n matrix as listed below

A =

1 1 1 . . . 1

1 3 3 . . . 3

1 3 6 . . . 6

…

…

…

. . .

…

1 3 6 . . . 3(n − 1)

(a) Use the appropriate row replacement operations to zero out the first pivot then use

the appropriate row replacement operations to zero out the second pivot column.

(b) Observe the resulting matrix from (a) is a block matrix of the form :

A =

[

X Y

0 Z

]

State your resulting matrix for X, Y and Z.

(c) Based on your result from (b), give a detailed set of steps to find det(Z).[

HINT: Take out a scaling factor for Z first then find det(Z).

]

EAST LA COLLEGE

DEPARTMENT OF MATHEMATICS

MATH 275 (ORDINARY DIFFERENTIAL EQUATIONS)

MINI PROJECT 3

SPRING SEMESTER 2020

INSTRUCTIONS — PLEASE READ!!

In this mini project, you are expected to provide a “typed cover sheet” of font size 12 using

“Times New Roman”, containing the course name, project number, your name, date and

your professor’s name using the correct title. The remaining pages must be labeled with the

following three components :

(1) Problem Statement (Must be typed)

(2) Background Information (Must be typed)

(3) Required Work & Solution (Hand-written or typed)

The “Problem Statement” is the given problem provided on the second page, which must be

typed by you rather than performing “cut and paste” from this pdf file.

The “Background Information”, should not focused on the given mini-project problem but it

should be more generalized and applicable to any problem, using your own words. Moreover,

it should explain the method used in solving the problem in a broad perspective and steps

needed to obtain a solution. So it should help someone learning this approach for the first

time, have a basic understanding of the steps needed to solve any problem of that particular

type.

The “Required Work & Solution” must contain all the necessary algebra work (written

neatly and easy to follow) in finding the solution. This mini-project is a representation of

your work and no one else.

This project is worth 30 points and must be submitted electronically to your professor using

Canvas email or ELAC email(carterdm@elac.edu), on or before 9:00am on June 1, 2020.

Late submission will not be accepted and receive a grade of 0%. You must submit your mini

project as one pdf file. Once you have electronically submitted your mini-project then your

professor will send you a confirmation email of that receipt within 12 hours. If you don’t

receive a reply from your professor then this means your email was not received and your

advised to submit it using the alternative email (ELAC email or Canvas email).

Moreover, if any background information or required work for the solution is viewed as

similar or identical, then the respective students will receive a 0%, which is considered

cheating. Also copying any work online for the solution is also classified as cheating and

won’t be tolerated. You are allowed to work together but a copy of another student’s work

or online work is not permitted. Your professor isn’t allowed to offer any assistance in this

mini-project nor check your unfinished mini project. Additionally, points will be deducted

for any messy work displaying scratch marks, and the like, or work that isn’t legible (such

as small script) or misspelled words or submission of your mini-project using a file that isn’t

classified as a pdf file or submitting more than one file.

Below you will find the problem for this mini project. Good luck !

Mini-Project 3

(a) Solve the following initial value problem

θy′′ + 2(θ − 1)y′ − 2y = 0 ; y(0) = 0, y′(0) = 0

(Give a simplified answer with positive exponents)

(b) Find a power series expansion about x = 0 for a general solution to the given

differential equation. Your answer should include a general formula for the coefficients.

(1 − x2)y′′ + xy′ + 3y = 0