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# Linear Algebra

### Matrices, Inverse, Transpose, Determinant, Gaussian Elimination and Cramer's Rule

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. 1. 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'

### Lines and equations

Answer problems on attached word document. Answer Questions If possible show work. I have a lot more questions to answer and I need to use examples to work through them. 1. Find the slope for 3y - 1 = 14 2. Find the equation of the line in the form y = mx + b if possible if the line goes through (2, -3) and (-3, 4)

### The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST.

Attached are problems involving linear equations. Thank you for your help. 1.) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring

### Matrices and Row Reduced Echelon Form

Please see the attached file for full problem description. 1. Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale and sell cookies (C), cakes (K), and muffin

### Prove that the fields R and C are not isomorphic.

Check if the proof is correct. I need help to justify some of my answers by using Theorems, Definitions and etc. You can change my wording but try to stick to my idea. It's really important that you explain your work. Thanks! Note: R=Real Number and C=Complex Number

### Angles, Systems of Equations and Gaussian Elimination

Two angles are supplementary of each other. Twice one angle is equal to the other angle minus the product of six and eight. A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.) B. Graph each of the equations on one rectangular coordinate system. (Hint:

### Provide a plot of temperature versus distance east. Based on its appearance, is it a good linear model for predicting temperature as a function of distance?

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 out the various areas and the friendliness for business. One of the factors of inte

### Word Problems Involving Linear Equations in Two Variables

1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floo

### Modeling with Linear Equations

There was several questions ask from my algebra class as a homework which I am having difficulty answering. Please help me solve for them thanks. The equation y = 1.13x + 7.85 represents the average monthly cost in dollars for cable television where x represents the number of years after 1980. Use this equation to answer the

### Solving Systems of Equations

1. y-2x=0 y=8x-9 What is the solution of the system of equations? (i need graph also) 2. r-6s=0 9r-8s=230 What is the solution of the system? 3. x+y= -13 9x+y= -61 What is the solution of the system? 4. (1,2); 6x-5y= -4 2x-7y= -12 is the given ordered pair a solution of the s

### Solving Linear Equations

Please see the attached file for the fully formatted problems. 1. Solve . You must show all work to receive full credit. Show work here: Final answer: 2. Solve . You must show all work to receive full credit. Show work here: Final answer: 3. A real

### solving system of linear equations using matrix method

1. Write the augmented matrix for the system of linear equations. a) 3x-2y+5z=31 x+3y-3z=-12 -2x-5y-3z=11 b) x-2y+3z=9 y+3z=5 z=5 3. write the system of linear equations represented by the following matrix. Use x,y, and z as variables: 4. Perform row operation and write the new matrix. 5. Solve the system of

### Solving Linear Systems of Equations with Matrices

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

### Word Problems and Systems of Equations

Train Tickets At the the Pittsburg zoo, children ride a train for 25 cents, adults pay \$1.00, and Senior citizens 75 cents. On a given day, 1400 passengers paid a total of \$740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders. Manufacturing St

### Algebra : Word Problems and Systems of Equations

Rowing Speed: Hank can row a boat 1 mi upstream (against the current) in 24 min. He can row the same distance downstream in 13min. If both the rowing speed and current speed are constant, find Hank's rowing speed and the speed of the current. Airplane Speed - An airplane flying with the wind from Los Angeles to New York Ci

### Systems of Equations and Inequalities Word Problems

Statistics. After reading an article on the front page of The New York Times titled "You Have to Be Good at Algebra to Figure Out the Best Deal for Long Distance," Rafaella De La Cruz decided to apply her skills in algebra to try to decide between two competing long-distance companies. It was difficult at first to get the compan

### Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.

Complete and please show all the work. Please see attached file for full problem description. 1. List all the factors of 45. 2. Which number is prime? A) 1 B) 12 C) 31 D) 99 3. List all the prime numbers between 25 and 60. 4. Find the GCF for 68, 85, and 153. 5. Find the LCM for 18 and 27. 6. Mul

### Matrix method to solve the linear system of equations

Please see the attached file. 3. A company's employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 22 carbohydrates and 14 grams of prot

### Environmental and wildlife preservation ensures future generations will have available resources and can enjoy the beauty of Earth.

I need to practice for an upcoming test. I am a little lost about how to do these. Any help will be appreciated. Please see attached file. Environmental and wildlife preservation ensures future generations will have available resources and can enjoy the beauty of Earth. On the other hand, some of the damage humans have al

### Linear Algebra: Hyperplanes

The equation 2x_1 + 2x_2 - 3x_3 + 8x_4 = 6 defines a hyperplane in R^4. a. Give its normal vector a. b. Find its distance from the origin using dot products. c. Find the point on the hyperplane closest to the origin by using the parametric equation of the line through 0 with direction vector a. Double-check your answer in

### MTH 212: Unit 4 Group Project - A

Using the attached file for full description: 1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .) A. By looking at the picture, d

### Linear equations and inequalities explained in this solution

Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch). Compute the vol

### Six lengthy questions on solving linear equations including word problems.

MTH212 Unit 1 - Individual Project A 1. Solve . You must show all work to receive full credit. Show work here: Final Answer: 2. Solve . You must show all work to receive full credit. Show work here Final Answer: 3. The cell phone service for the CEO of a small company is \$39.99 a month plus

### The cell phone service for the CEO of a small company is \$39.99 a month plus \$0.10 per minute for long distance.

Using the attached for full description. 1. solve 2(x - 4) = 2[x - 3(x -1) + 2]. You must show all work to receive full credit. 2. solve (x -2) /3 - (x + 5)/6 = (5x -2) /9 3. The cell phone service for the CEO of a small company is \$39.99 a month plus \$0.10 per minute for long distance. In a month when the company's ph

### Equation of Motion: Spring Mass System Example

Please see attached for question and diagram. A certain engineering system can be represented by mass in a spring, as shown in Figure 1. If the mass is pulled downwards and then released, it oscillates on the spring. Using Newton's second law, a homogeneous second-order differential equation can be set up as below (see attach

### The solved problems involve forming matrix equations for word problems, Solving system of Linear equations using matrix method, Gaussian Elimination method, Cramer's Rule. It is also explained and worked out how to write the coefficient matrix, find inverse of matrix, Transpose of matrix, finding cofactors of elements of matrix and determinant of matrix. For the original problems solved in this posting, please refer the Ling description(original problems solved) Suppose a form 1040EZ requires \$12 in computer resources to process and 22 minutes of the accountant's time.

Deliverable Length: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 a

### Linear Programming : Optimizing using Matrix Methods

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 and linear equations

Need help in understanding what is going on with this problem: 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 sol

### Linear Algebra : Orthogonal Basis

Please see the attached file for the fully formatted problems. Problem a. quote a theorem which guarantees that there exists an orthogonal basis for (with standard inner product) made up of eigenvectors of matrix b. Find such a basis . c. Represent the quadratic form by a symmetric matrix. Is Q positive definite?

### Systems of Equations and Reduced Row Echelon Form

1) Solve the system using row echelon form 2x-3y+2z=-3 Please show step by step. -3x+2y+z=1 4x+y-3z=4 1b) Solve the system y=x^2-2 & 3x-y=1