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Linear Algebra

Systems of Linear Equations

Module 3 - Case Systems of Linear Equations Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong. 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6

Quantitative Methods Linear Equation a-f

5) A small manufacturer produces special order DVDs for individuals and businesses. The materials and labor costs for each DVD is $0.25. The fixed costs of production are $525. The manufacturer charges a client $5.00 for each DVD. Suppose x denotes the number of DVDs produced and sold. Use the information above to find the follo

find eigenvalues and vectors

See the attached file, please. Given the following matrices A, B, and C compute the eigenvalue and eigenvector for each matrix. A =(-2, 6, 6, 3) B= (4, 2, -1, 6) C= (0, -1, 1, 2)

Linear equations and word problem

Please help with the following problem. 1. Sharing fruit Apples are collected in a basket for six people. One third, one fourth, one eighth, and one fifth of the apples are given to four people, respectively. The fifth person gets ten apples, and one apple remains for the sixth person. Find the original number of apples in

Solve linear problems.

consider the line -8x-2y=-5 what is the slope of a line perpendicular to this line and what is the slope of the line parallel Suppose that the weight in pounds of an airline is a linear function of amount of fuel (in gallons) in its tank when carrying 20 gallons of fuel, the airplane weighs 2030 pounds, when carrying 54 gall

Find the slope of the line shown and interpret the slope.

Find the slope of the line shown and interpret the slope as a rate of change given the following information. I am supposed to present this in business terms using Exxon Mobile as the example and using the mathematical concept of slope and rate of change. After submitting this question earlier I am not sure the answer is what I

Truth tables are exemplified.

1. Let p, q, and r be the following statements: p: Sylvia is at the park. q: Jamie is on the train. r: Nigel is in the car. Translate the following statement into English: (~q / p) -> ~r 2. Construct a truth table for ~q -> p. 3. Construct a truth table for (p / ~q) ↔ q. 4. Let p

Show divisibility.

1. Emperor's Banquet You have been invited to the emperor's banquet. The emperor is a rather strange host. Instead of sitting with his guests at a large round dining table, he walks around the table pouring oatmeal on the head of every other person. He continues this process, pouring oats on the head of everyone who has n

Proof for Non-Empty Subsets

Please help with the following problem. Use the following steps to prove that every non-empty open subset of R is a union of at most countably many disjoint open intervals. Suppose that G is a non-empty open subset of R. 1. For each a <- G let Ia be the union of all those open intervals I which contain a and are containe

Systems of Linear Equations - Graphs

Answer the question and solve the problems below. Make sure you show all your work. 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 2. Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the num

Linear regression model

Senior Management at Esil University believes that decreases in the number of undergraduate applications that they have experienced are directly related to tuition increases. They have collected the following enrollment and tuition fees data for the past decade: Year: Undergraduate Applications: Annual Tuition

Linear algebra word problem

A discrete dynamical system model for the population of cheetahs and gazelles in Namibia is given by the following pair of equations: .3Ck + .4 Gk = Ck+1 -pCk + 1.3 Gk = Gk+1 where Ck measures the number of cheetahs present in a certain Namibian game reserve at time K, Gk gives the number of gazelles (measured in tens),

Linear Algebra: Systems of Equations

Please show all work for the attached questions. 8. A cellular phone company offers a contract for which the cost c, in dollars, of t minutesof telephoning is given by C= 0.259t-300)+79.95, where it is assumed that >300 minutes. What time will keep cost between $129.95 and $167.20? - For the cost

Computer graphics and linear algebra

Why is linear algebra important for computer graphics? How are linear algebra techniques used in computer graphics? Please review the following link,Mathematics for Computer Graphics, Retrieved February 29, 2008, from and Matrices, Retrieved February 29, 2008, from http:/

Systems of Linear Equations

We will be looking at a common application of linear algebra in sociology and psychology, the domination matrix. Click on the links below and read through the descriptions of these applications: Domination Matrix, Retrieved February 29, 2008, from Gr

Determining if a System as Stable or Unstable

Please show steps to evaluate for correct answer. 1. Systems are unstable if their characteristic equations have a positive root (solution). Determine whether each of the following characteristic equations represents a stable or unstable system. (i) s^3 + 6 s^2 + 11 s + 6 = 0 (ii) s^3 + s^2 - 8 s - 12 = 0 2) In a Hook

Goldbach's conjecture

One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows: Every even integer greater than 2 can be expressed as the sum of two (not necessarily

Eigenvalues and Transformations

Please show the complete steps. 1. Let T: P2 -> P1 be the linear transformation defined by T(p(x)) = p'(x) + p(x). Show that T is linear. 2. Find the matrix for the transformation T given in problem 1 with respect to the standard basis {1, x, x^2}. Then, find all eigenvalues and corresponding eigenvectors for T. 3. True

Systems of Linear Equations; Matrices

Part I (refer to the section on Systems of Linear Equations; Matrices in your text): As a restaurant owner there are many decisions that you need to make on a daily basis, such as where to keep inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have two dish design

Solving for Systems of Linear Equations

Create a system of linear equations from my own life. Keep in mind that a system of linear equations will consist of two equations using the same variables and the variables will represent the same thing for both equations, i.e., if you use X as a variable in the first equation and X represents a number of Beers then you need to

Linear Equations & Functions

Good morning - my son has chapter test tomorrow and on linear equations. I would love to be able to help him study, unfortunately is been a while since I've done linear equations and my knowledge is sketchy at best. Attached is a study guide that he will be using to study from. Can you please solve the equations and provi

Linear algebra

(A paradox) Suppose A has a right-inverse B. Then AB = I ... see the picture please. Thank you.

Discussing Functions and Linear Equations

Hi, I need some assistance computing the following mathematical questions so that I can create a study guide. Answer the following questions and if required, do calculations to please show your work: 1. What is a function? 2. What is a linear function? 3. What form does a linear function take? (e.e., What is the

Matrix in reduced row-echelon form, Solving system of equations,

1). Write the matrix in reduced row-echelon form: [1, 2, -1, 3], [7, -1, 0, 2], [3, 2, 1,-1]. 2) Find the equation of the parabola that passes through the given points. Use the graphing utility to verify your result. (Please look at the picture). 3) Use a graphing utility to find AB, given. A= [1, 3, 6], [4, 1, 3] B= [0, 1

Demand equation. Helen's Health Foods usually sells

Please answer the enclosed 6 questions and use EXCEL for graphs. Please answer the following questions....all graphs must be done in EXCEL. Question#1 Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is $5 per can. After experimenting with prices for some time

Linear equations in business

Why is it important to understand linear equations in business? In particular can you provide examples where the relationship between items that can be affected by management and 'items' that management wished to achieve or attain may be 'linear'? Can you think of items for which the relationship is NOT linear?