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Linear algebra

3 pages (750 words)

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... Proposed Research Topic: The Role of Linear Algebra in Projecting the Success of a Web Based Business Purposes: For many people, students and non-students alike, the essence of Linear Algebra is not much appreciated with the knowledge that this subject is only for those who are specializing in mathematical studies. On the contrary, mathematics is an everyday experience for us though usually not greatly observable. It is the goal of this research to let linear algebra be employed in the famous world of business, where else but the use of internet. This would be an interesting field to apply the study of linear algebra as it gives a twist to the misconstrued perception that linear algebra is just...

Teaching and Learning Algebra

4 pages (1000 words)

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... and Learning Algebra Most find it difficult to understand and apply algebra, especially when first introduced to the This paper examines some of the reasons for this and focuses specifically on student difficulties with three major algebraic issues.
Students’ Persistent Algebra Difficulties
The National Curriculum has for many years set forth standards for teaching algebra to students from ages younger than 16 years through 19 years. An extensive analysis of the impact of these standards was conducted by the Joint Mathematical Council and The Royal Society during 1994-1997. It concluded that the standards were not achieving adequate results from students, and made many recommendations for improve...

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College Algebra

2 pages (500 words)

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... Affiliation Algebra Questions chosen are question 2, 4 and 5 Question 2 The degree of the function x2(x-2)3 canbe determined by first expanding the function and then the terms are put in decreasing order of their exponential. . The function is then expanded as shown below.
The expansion of (x-2)3 is first done and the result multiplied by x2
x2(x-2)3
x2(x3- 6x2 + 12x - 8)
x5- 6x4 + 12x3 - 8 x2
The coefficients of the function are not necessary for the determination of the degree of the polynomials, therefore they are ignored and the equation rewritten as:
x5- x4 + x3 - x2
The power of the largest term is then identified. For this function, the largest term is the first term with the power of 5.
T...

Algebra

1 pages (250 words)

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... Algebra Answer Part Expand along the first row, In terms of symbol the cofactor is, Now, we put all the quantities for the entries. For the cofactors we will put the minor and a (“+1” or a “-1”) which depends on sign required for each minor. This signs will be by going to our “sign matrix” above beginning at the 1st entry in the particular row or column we are expanding along (Larson, & Falvo 110). After that as we move on that column or row we will put the sign required in that case.
Part 2
Expand along the first column,
In this case symbol form of the cofactor is,
Here the signs of “a” are similar to the above case the first row and column have identical signs;
Part 3
In this case we will cofacto...

Algebra

3 pages (750 words)

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... There are a number of ments that are equivalent to the following: The n x n matrix A is invertible. Four equivalent ments are given below:
1) The determinant of A is not equal to zero.
2) The equation Ax=0 has only the trivial solution.
3) The equation Ax=b has at least one solution for each b in Rn
4) A is row equivalent to the n x n identity matrix.
Part I
Six additional statements:
5) A is expressible as a product of elementary matrices.
6) Matrix A is square
7) The columns of A are linearly independent.
8) The columns of A span Rn or Column A = Rn
9) The columns of A form a basis of Rn.
10) Rank A = n.
Part II
1) Matrix A has a non zero determinant because Matrix A is invertible. An invertible...

Algebra

4 pages (1000 words)

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... I: Linear Algebra and Geometry Assignment: Give a detailed of how linear transformations can be used to study rotated conic sections. Your essay should include:
1) A description of rotations through an angle about the origin.
Each of the conic sections which are centered at the origin can be described by the equation
Ax2 + Cy2 + Dx + Ey + F = 0
This curve can be rotated through an angle about the origin by using the rotation equations:
x = x’ cos - y’ sin
y = x’ sin + y’ cos
so that the transformation matrix is:
R =
cos
- sin
sin
cos
These values for x and y are substituted into the equation of the curve in order to obtain a new equation for the curve in terms of t...

Algebra Math Problem

6 pages (1500 words)
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... Final Project The system of linear equations may be applied to mixture problems in which itemsof various types or grades are sold at distinct values. This is particularly useful for starting entrepreneurs who consider establishing business on a small-scale with simple calculations carried out. Application: Matthew would like to put up a small coffee-bean store selling two special varieties of coffee – Arabica(M) and Robusta(H). He estimates obtaining profit from each kg of Arabica(M) worth $10.50 and from each kg of Robusta(H) costing $9.25. If he desires to have 2500 kgs of bean-mixture sold for $9.74 per kg, how much of each kind must be present in the mixture? Solution: Let x = the quantity of...

Algebra for Business

1 pages (250 words)

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... for Business: Types of systems: Inconsistent or Dependent Corse Algebra for Business: Types of systems: Inconsistent or Dependent
Systems of equation with one or two variables are very helpful in solving every day problems. In business these systems can be used to solve complex mathematical function with simple steps and algebra. On the other hand the graphical representation allows viewing the future values.
Consider two equations with two variables: x and y,
5x + y = 13
4x + 4y = 20
We can easily solve the system of equations and attain the results in the pint form so that the two lines collide at a point in graph. In general form, the graph is such that:
This is the general form.
Inconsistent ...

Assessment Plan on College Algebra

5 pages (1250 words)

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... Plan on College Algebra The paper aims at analyzing the learning outcomes in the area of college algebra, and also developing an assessment plan to enhance the understanding of college algebra. The student learning outcomes are generated through accumulated academic competencies that include; knowledge, attitude and skills of the students. These academic competencies are developed through the academic study process. Learning outcomes entails wider aspects of program that include wider elements; for instance, graduation levels, faculty levels academic publications, and eventually job placement (Hitchcock, 2011). The learning outcomes in the area of algebra aim at addressing five key issues. Firstly,...

Algebra week 7

1 pages (250 words)

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... 20 June Algebra Question 12 In a graph of y against x where x includes the variables that form an equation of y to x, an increase or decrease in x values result into a considerable change in the upward or downward opening of the graph. The graph opens up when x gets more and more positive (Knapp, 20). That is, a positive increase in x values results into positive increase in the y value thus makes the graph to move upwards (open up). On the other hand, when x values get more and more negative the graph opens down. That is, as the values of the variable x get more and more negative, it consequently results in the reduction of the y value. Thus this leads to the graph to move downwards open down...

Algebra

4 pages (1000 words)

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... Evaluating Algebraic Expressions: use the birth or the birth highlighted in yellow Write your birth or the birth someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). 11/2/82
Now let a = the one- or two-digit month number,
b = the negative of the one- or two-digit day number, and
c = the two-digit year number.
(Our example: a = 3, b = -13, and c = 81 or a = 11, b = -7, and c = 67)
a = 11, b = 2, c = 82
2. Use the following algebraic expressions for parts c-d of the discussion:
113 – (-2)3
1331 – (-8)
1339
(a-b) (a²+ab+b²)
(11 – (-2))(112 + (11*-2) + (-2)2)
(11+2)(121 – 22 + 4)
(13)(103)
1339
3. Evaluate the three given expressio...

Digital Signal Processing and Linear Algebra

4 pages (1000 words)
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... Application of linear algebra in Digital signal processing There are various scenarios in which linear algebra isused in solving real – life problems. The applications ranges from different fields which include net flow, economics and chemistry. Linear algebra has been extensively used in signal processing both theoretically and algorithmically. The interaction between linear algebra and and digital signal processing has resulted in development of new algorithms in digital processing. This is basically focused in development of linear algebra tools which include things like recursive least squares, total least squares, eigenvalues, projections, orthogonality among others. To add on this, the use of...

College Algebra

6 pages (1500 words)

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... B of Object Circumference (c) Diameter (d) Circumference divided by diameter (c/d) Large coffee mug 12.21 in 3.50 in 3.48 in Sports bottle
10.31 in
3.00 in
3.44 in
Regular drinking glass
9.81 in
2.50 in
3.92 in
The value of pi, 3.14, is a mathematical constant in which the circle is defined. The value of pi is found through calculation of the circumference divided by the diameter. The size of the object does not vary because the ratio between the circumference and the diameter is always constant to 3.14. When manufactures make a glass, a coffee mug, etc., the ratio is kept the same due to the constructs of the circle. This is because it remains constant.
With my calculations, I discovered that I h...

3 lesson plans for algebra

6 pages (1500 words)

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... Lesson Plans by JT Thomas 6-21-2006 Lesson Multiplicative Inverses Introduction The purpose of this lesson is to introduce tothe concept of multiplicative inverses. By using the fact that 0 doesnt have a multiplicative inverse, it is shown that division by 0 is not defined.
2.Introductory Examples
To find a multiplicative inverse of a number x, we must find the number that when multiplied by x, equals 1:
x * (multiplicative inverse) = 1
This number is always the reciprocal 1/x, since after canceling x in the numerator and denominator we are left with 1 multiplied by 1:
x * (1/x) = 1 * 1 = 1
For instance, to find the multiplicative inverse of 6, we just divide 1 by 6:
6 * (1/6) = 1
3.Expositio...

Algebra-Unit 1

3 pages (750 words)

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... Length: 2 – 5 pages Instructions: Type your answers next to the yellow text. o For noninteger answers, please write your answer as a fraction rather than a decimal.
To show your work, you will need to include
o the algebra used to compute the solution to any equations.
o the formula with substituted values.
o the final calculated answer with units.
MTH212
Unit 1 Individual Project - B
1. Solve . You must show all work to receive full credit.
Show work here:
Final answer: x = 6
2. Solve. You must show all work to receive full credit.
Show work here:
Final answer:
3. A real estate broker’s base annual salary is $18,000. She earns 3% commission o...

Applications of Linear Algebra to Electrical Engineering

6 pages (1500 words)
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... of Linear Algebra to Electrical Engineering
Engineering is heavily influenced by the mathematics. Engineering problems can be solved by utilizing the principles of mathematics. Calculus, algebra, etc are the branches, which are utilized in the Engineering problems. We can say that the practical application of the mathematics can be truly seen in the engineering problems. The examples can be seen when derivation and integration are utilized to resolve the electronic and electrical circuits. Linear Algebra is also utilized to solve the problems. Matrices are used to find the simplest method of solving complex electrical circuits. A mesh is loop that has a single current flow path. In the circuits wh...

Seventh Grade Algebra and Learning through Experience

4 pages (1000 words)

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... Head: LEARNING THEORY Seventh Grade Seventh Grade Algebra and Learning through Experience Seventh Grade Algebra and Learning through Experience Introduction The learning outcomes of seventh graders who are given the opportunity to learn algebra are defined by the previous knowledge that each individual has about mathematics. Through understanding Piaget’s theories on learning, it is clear that in order to progress into learning how to do algebra, a student must be able to draw upon what they have learned in the past and how they learned to process the logic of what is being taught. In addition, it is clear that through teaching with the experience of doing, a student will learn at a higher and more...

COLLEGE ALGEBRA-DISCUSSION BOARD

1 pages (250 words)

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... Algebra-Discussion Board The Euler’s number e is one of the most important constants in mathematics. The constant is approximately 2.71828182845…; however, the number has been estimated to a fairy high degree of accuracy. Being a rational number implies that e has indeterminate decimals. The Euler’s numbers servers as the base to the natural logarithm.
The Euler’s constant can be derived through several methods and each of these methods depends on the intended use. The first method is based on the infinite series theory. From this method e is the limit of (1 + 1/n) {n± 0} or (1 + 1/n!) as n tends to infinity. Therefore e = 1 + 1/1 + ½ + 1/3 + ¼ …. Alternatively, e =1 + 1 + 1/ (1× 2) + 1/ (1 × 2 × 3...

Algebra Week 11

1 pages (250 words)

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... fractions are fractions that can include a numerator, denominator and an extra number. In this case, the simplification of a mixed fraction is done by converting it into an improper fraction and then converting into integers. To simplify 16 1/2, multiply 16 and 2 and the result will be 32, which is summed up with 1 which gives 33/2. This improper fraction can be further simplified by finding the quotient of the equation, which is a number with a decimal point, 16.5 (Szecsei, 2006)
Simplifying the square root of 100 will be equal to finding the number which when multiplied by itself give 100. The first step in simplification is writing the statement in the basic format, which is √100. In this, the be...

Everyday life with Algebra in the Real World

4 pages (1000 words)

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... Everyday Life with Algebra in the Real World Table of Contents page…………………………………………………………………………………………………..1 Table of contents………………………………………………………………………………………….2 Algebra applied to science………………………………………………………………………………3 Algebraic concepts to solve everyday problems………………………………………………………3 Algebra applied to personal life………………………………………………………………………...4 Surprising finding about how algebra affects personal life…………………………………………...5 References………………………………………………………………………………………………...6 Algebra applied to science In science, algebraic methods of computation are applied in the study of biological problems, particularly in the study of genes, proteomics, genomics and analysis of molecular structures. In the...

How College Algebra is used in the Nursing Field

5 pages (1250 words)

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... How College Algebra is used in the Nursing Field al Affiliation How College Algebra is used in the Nursing Field Algebra is a branch of mathematics that deals with vector space, infinite dimensions and general linear mappings between given spaces. All this is achieved through the system of linear equations that contain a number of unknown variables; mostly represented in the form of vectors and matrices. Thus, the techniques obtain from linear algebra are used in various fields. These fields include engineering, nursing, natural sciences, social sciences, computer animation, physics, computer science and analytical geometry. Across the globe, the numbers provide lots information to be used by the...

LINEAR ALGEBRA

1 pages (250 words)

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... LINEAR ALGEBRA QUESTIONS Question 7 marks] é1 2 ê 5 b ù ú é1 2 0 3 ù ê ú The reduced row echelon form of
A = ê4
a 17
- 22ú is equal to R = ê0 0 1
- 2ú .
ëê row3 úû
êë0 0 0
0 úû
(a) What can you say about row 3 of A? Give an example of a possible third row for A.
This is a null row representation that the results become zero due to the figures of R which are equivalent to zero.
(b) Determine the values of a and b.
{1, 2, 5, 1} {b} = {1, 2, 0, 3}
{4, 1, 17, -22} {a} = {0, 0, 1, -2}
B=1
A =0
(c) Determine the solution of the homogeneous system of equations Rx = 0 in parametric vector form.
Rx = 0
Row 3 – {0, 0, 0)
(d) What is the dimension of the column space of A? Do the columns of A span ...

DIOPHANTUS A KEY FIGURE IN THE HISTORY OF ALGEBRA

4 pages (1000 words)

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... A Key Figure In the History of Algebra Algebra The history of algebra can be raced back to the ancient Egypt and Babylon where people learned the basics of solving various equations that include the linear equations, the quadratic equations and the indeterminate equations. The oldest mathematical documents that are found in ancient Egypt can be dated back to 1900 B.C. quadratic equations today are basically solved logically using the same procedures/methods that the ancient Babylonians used (The Brussels Journal, n.d).
Diophantus
Diophantus of Alexandria (also known as the father of algebra) was born in 210 and died in 290. He was a Greek mathematician who was born, raised and lived in Alexandria in ...

Evaluation of the Effectiveness of the Different Methods of Teaching Algebra

2 pages (500 words)

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... OF THE EFFECTIVENESS OF THREE DIFFERENT METHOD OF TEACHING ALGEBRA (Your School's , the school where I work as a teacher, has an enrichment program to teach algebra to students weak in this area. Three teaching methods have been identified that could be used to improve students' skills in this area. The first is the traditional classroom teaching method (A), the second method incorporates visual tools and models such as graphic calculators (B), and the third method incorporates games such as chess (C).
I conducted an experiment designed to evaluate the effectiveness of the above three different methods of teaching algebra. Participating students were randomly assigned to one of the three treatmen...

Matrix Analysis Linear Algebra SVD

8 pages (2000 words)

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... Matrix Analysis Linear Algebra SVD 1a Compute the residue matrices Rj,k associated with λj. Our aimis to show that it is almost diagonal. We recall that Rn is a circulant matrix. This is approximated by circulant matrices R (z) and can be written as the sum of two circulant matrices, plus some error that will be bind. To define two circulant matrices Rj,1 and Dj,1, we observe the upper right upper side of the circulant matrix.
It is recalled that often, we may transform the data because it may be easier to analyze the transformed data. The same applies here.
1b.) A=∑j=1h(λjPj+Dj)
Let A be a self-adjoint matrix, A = A* with spectral decomposition above. Then
(zI-A)-1=∑λ\ σ(A). (1/z-λ)Pλ, for all z ∈ C...

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