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Linear Algebra

An art dealer sold two artworks for \$1520

An art dealer sold two artworks for \$1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for \$1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork. A professor starte

Discussing Eigenvectors and Eigenvalues

Assume that ST = TS. Prove that the operators S and T have a common eigenvector. Let V be a complex (i.e. F = R) finite dimensional vector space. Let S, T be elements of L(V ) (set of operators on V). Assume that ST = TS. Prove that the operators S and T have a common eigenvector. these are the steps: a) Explain why T

To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T).

MTH212 Unit 3 - Individual Project A 1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The num

Applications of Linear Equations

The director of a summer day camp estimates that 120 children will join if the camp fee is \$250, but for each \$25 decrease in the fee, five more children will enroll. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the lin

Eigenvalues and Generalized Eigenvectors of a Matrix

Please see attached file for full problem description. a) Find the eigenvalues and (generalised) eigenvectors of the matrix 1/3 -11/15 7/15 A= -10/3 26/15 23/15 5/3 -7/15 14/15 and hence find eAt.

system of linear equation and compound inequality

Please see attached file for full problem description. Solve system by the substitution method. 1. y = 2x - 6 y = x - 5 2. 7x - 4y = 26 y = x - 5 ------------------------------------------------------------------------------------ Solve each system by the addition method. If there is no solution or an

Algebra : Area and Writing Equations from Word Problems

Please see the attached file for all of the problems. 12. Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m and the area is 224m2, find the length of the other base. 13. The sum of two consecutive integers is 145. Find the two integers. 14. Yuri has a board that is 98

Systems of Equations Word Problems

Please see attached file for full problem description. 1. Two cars leave a restaurant at the same time and travel in opposite directions. One averages 50 miles per hour and the other averages 40 miles per hour. After how long will they be 216 miles apart? 2. How many gallons of a 4% acid solution should be mixed with 2

Row Operations and Reduced Row Echelon Form

Rewrite the following system of equations as an augmented matrix. Put the matrix in reduced row echelon form to find the solution to the system of equations. x-y=3 6x+7y=44 6x-7y=16 This is as far as I got, then I am unsure of what to do next 1 -1 3 6 7 44 6 -7 16.

Mathematics - Linear Operators explained in this solution

1. solve the following equations and show work. 2. You are given the following system of linear equations: x - y + 2z = 13 2x + xy - z = -6 -x + 3y + z = -7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this mat

Matrix Solutions to Systems of Linear Equations

Matrices are the most common and effective way to solve systems of linear equations. However, not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution. For this Discussion Board, provide an example of a matri

Matrices - Matrix methods can be used to solve linear programming problems. For specific problems, please see the posted problems.

3-6 pages 1. Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires \$12 in computer resources to process and 22 minutes of the

Linear Programming Problems: Tax Returns

Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires \$12 in computer resources to process and 22 minutes of the accountant's t

Matrices, Solutions and Systems of Equations

Not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution. Matrices are the most common and effective way to solve systems of linear equations. Provide an example of a matrix that has no solution. Use row oper

Stability of systems

1. A single-loop negative feedback system has a loop transfer function. GH(s) = K(s+2)^2 / s(s^2+1)(s+8) Determine the range of the gain K for which the system is stable. Choose either a. 23 < K < 367 b. K > 14 c. 0 < K < 5 2. A system has a characteristic equation q(s) = s^4 +9s^3 +45s^2 +87s +50 +0. De

Applications of Linear Equations

Task Name: Phase 2 Individual Project Deliverable Length: 10 slides with notes Details: Your company was very impressed with your results from the recent study. They have asked that you investigate another location for them and present this new promising location at the upcoming sales meeting. Again, it is your job to check

Linear Equation and Inequality

I need help in showing what the graphs look like and what the differences are for the following scenario: Preparing for upcoming sales meeting and need to create and compare various supply demands by graphs to show the break even point for the company. You have compared the linear equation graphs and linear inequalities. What a

Linear Equations and Inequalities

Part 1: Using the Library, web resources, and/or other materials, find a record-breaking temperature (in degrees Fahrenheit) for a town or city of your choice. Include the name of the town, along with the temperature, and what record was broken. Give the formula for converting degrees Fahrenheit to degrees Celsius. Using the fo

Linear Algebra Problems in MTH 212 Unit 1 Individual Project - B

See attached file for full problem description. 1. Solve -3[5+2(-7+x)+x]=-3x-(x+3). 2. Solve -(4x+4)/5 = (5x -1)/2 - x/3. 3. A real estate broker's base annual salary is \$18,000. She earns 3% commission on total sales. How much must she sell in real estate value during the year to earn \$65,000? Set up an equation and

Linear Programming and Matrix Reducing to Row Echelon Form

1. The Copperfield Mining Company owns two mines, each of which produces three grades of ore-high, medium, and low. The company has s contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore d

Systems of Equations

1. Write an equation of the line that passes through (0, -4) and is parallel y = (3/4)x + 2. Write the answer in slope-intercept form. 2. Solve the system of equations by substitution: x + 2y = 9 3x - y = 13 3. Solve the system of equations by substitution: 4x - 3y = 1 12x - 9y = 3

Linear Programming

Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x

Equations of Lines and Solving Systems of Linear Equations ( Simultaneous Equations )

1. Find the slope of the line that passes through the points (2, 3) and (5, 8). 2. Find the equation of the line that passes through the points (3, -2) and (4, -2). 3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 6 and passing through (-3, 5). 4. Solve the

Solving and Graphing Systems of Equations and Inequalities

I need to know how to graph the following inequalities: 3x + y = or <5 x-y= or <2 y= or >5 Solve the system by graphing: x-y=2 3x-3y=6 3x-y=1 3x-y=2 Solve the system of linear inequalities by graphing: x-2y= or <4 x->1

Graphing linear inequalities

Solve the following system of linear inequalities by graphing. 3x+4y is less than or equal to 12 x+3y is less than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0

Linear Programming, Equations of Lines and Word Problems

1) f(x)=3x(2x-1). f(-1)= A)7 (B)11 (C)-6 (D) 9 2) The slope of the line through the points (3,4)and (-1,7) is A)4/3 (B) ¾ (C) -3/4 (D) 7/4 3)The line 6x + 9y=8 has slope A) -2/3 (B)-6 (C) 4/3 (D) 9 4)Select the line parallel to 6x +14y =20 A) 3x-7y=15(B) 7x-3y=8 (C) y=20/6x+14 (D)y= -3/7x+11/7 5) A revenue f

Linear Equations and Systems of Equations with Parameters

Please help with the following problems. Provide step by step calculations. Find the slope of each line that has a slope x=5y Find an equation in the form y=ms +b (where possible) for each line. Through (3,-5) parallel to y= 4 Graph each linear equation defined as follows; 3x - 5y =15 Solve each system of equat

Matrices

Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them. Copy the questions to a Microsoft Word document and use an equation editor to enter the answers. Please answer the following questions

Finite Mathematics - Finding Equation of a line, break-even point, Revenue function, Cost function, Salvage value, Scrap value, system of equations, Augmented matrix, Matrix, Matrices, solution of system of equations, Input-out matrix, linear programing, feasible region, inequalities, Objective function, Maximization, Minimization, dual problem, Initial Simplex Tableau, Pivoting, feasible solution, compound interest, compounded semi annually, Annuity, Future Value, Periodic Payment, Accumulation Factor, Sets, Intersection, Union, problems, Permutations, ways of arrangements, Combinations, ways of selections, Probability, Standard Deviation of grouped data, formula, confidence level, upper bound.

Note: For detailed description of the questions, please see the attached questions file. Below is the text that represents the brief description of the actual questions. Question (1) Given, f(x) = ( x + 2 )(2x - 3) , f (- 2 ) = ? Question (2) The equation of the line through (8 , 6 ) and (2 , - 4) is ... Question (3)

Eigenvalues, Heat Equations and Parseval's Identity

See attached file for full problem description. You can solve problems except matlab problems(1.(c),3(c),6(d,e)). But I still hope you would solve all problems including matlab problems. And you can send me solutions separating into two parts regardless of problem's order.