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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... ...

Algebra

4 pages
(1000 words)

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...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... Part I: Linear...

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Algebra

3 pages
(750 words)

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...algebra, an n-by-n (square) matrix A is called invertible, non-singular, or regular.
If an n-by-n matrix exists the matrix must be square.
6) A is expressible as a product of elementary matrices, because every elementary matrices are invertible and its inverse is also an elementary matrices. A square matrix is only invertible if it can be written as a product of an elementary matrix.
7) A family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. An alternative method uses the fact that n... Given: There are a number of ments that are equivalent to the following: The n x n matrix A is invertible. Four equivalent...

Algebra

4 pages
(1000 words)

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...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... Discussion Evaluating...

Linear algebra

3 pages
(750 words)

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...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... Full Proposed Research Topic: The Role of Linear...

College Algebra

2 pages
(500 words)

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...Algebra 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...

College Algebra

6 pages
(1500 words)

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...algebra we find measurements using lines.
The best approximation for inscribing the polygon was once... Assignment 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 ...

LINEAR ALGEBRA

1 pages
(250 words)

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...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...

College Algebra

6 pages
(1500 words)

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...algebra we find measurements using lines. The best approximation for inscribing the polygon was once... ?Assignment 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...

Teaching and Learning Algebra

4 pages
(1000 words)

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...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... Teaching and Learning...

Algebra week 7

1 pages
(250 words)

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...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... 20 June...

Algebra Math Problem

6 pages
(1500 words)
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...algebraic expressions in which variables are made to represent unknown amounts of objects either count or non-count by nature. I appreciate the fact that in Algebra, one is able to verify the existence of a solution by using methods of elimination and substitution wherein one method can be a means to countercheck the other which ought to show the same results. It is quite interesting that equations may... 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....

Algebra for Business

1 pages
(250 words)

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...Algebra 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...

Assessment Plan on College Algebra

5 pages
(1250 words)

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...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... Assessment Plan on College...

Algebra-Unit 1

3 pages
(750 words)

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...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... Deliverable 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 alg...

Algebra Week 11

1 pages
(250 words)

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...Algebra. USA: Book-mart Press.... Mixed 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 for...

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...

ALGEBRA

1 pages
(250 words)

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...1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project. a) Write an inequality that demonstrates how much money you will be willing to spend on the project.
Ans. 6000 x 10000
b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500 Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
Ans. 8
60r + 84t 2500 where r... You are...

3 lesson plans for algebra

6 pages
(1500 words)

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...Algebra 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...

Matrix Analysis Linear Algebra SVD

8 pages
(2000 words)

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...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... Matrix Analysis Linear...

Applications of Linear Algebra to Electrical Engineering

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(1500 words)
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...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... Applications of Linear Algebra...

Digital Signal Processing and Linear Algebra

4 pages
(1000 words)
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...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... Application of linear...

Seventh Grade Algebra and Learning through Experience

4 pages
(1000 words)

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...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... ?Running Head: LEARNING THEORY Seventh Grade Seventh Grade...

Everyday life with Algebra in the Real World

4 pages
(1000 words)

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...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... ? Everyday Life with Algebra...

DIOPHANTUS A KEY FIGURE IN THE HISTORY OF ALGEBRA

4 pages
(1000 words)

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...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... Diophantus A Key Figure In the History of Algebra ...

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