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# Linear Algebra

### Linear Transformations, Matrices, Projections, Reflections, Kernels, Vector Space, Rank and Nullity (11 Problems)

Please see the attached file for the fully formatted problems. 1 Prove that the solution space of AX = 0, where A is a m x n matrix, is a vector space. 2 Are the vectors x3 - 1, x2 - x and x linearly independent in P3 ? Why ? 3 Determine whether or not the function T : Mmn --> Mmn de ned by T(A) = A + B, where B is a mix

### Business : Formulate and Solve Systems of Equations for a Real-World Problem

The financial institution has asked your firm to place some spot advertisements. The financial institution wants you to find the best allocation of ads between 2 of the local media outlets. The company you have chosen to handle the transaction has estimated the average number of potential new customers reached per spot annou

### How Matrices Are Used to Solve Equations

1. Guassian Elimination is really just using the regular Elimination Method and applying the Triangular Form procedures to a set of linear equations, but without having to write down all the variables in the equations each time. This in itself simplifies the procedure and helps focus on the task. What is the ultimate goal of all

### 20 Algebra Problems : Solve for X, Percentages, Perimeters and Simplification

Please see the attached file for the fully formatted problems. Use the appropriate property of equality to solve each equation. 91. 5a = -10 7 93. 1 v = - 1 v + 3 2 2 8 Solve each equation. 77. 7- 3(5 -u) = 5(u - 4) 85. 4 - 2n = 12 5 90. 3(x - 0.87) - 2x = 4.98

Please see attachment. *1. Disregard 2. Simplify the following expression: 3. The surface area of a right prism is given by , where is the area of the base, is the perimeter of the base, and is the height of the prism. Solve for . 4. Solve the following equation for . Simplify your answer

### Linear programming blending problem using Excel Solver Table.

NewAge data Cost/lb of chemicals Chemical 1 \$8 Chemical 2 \$10 Chemical 3 \$11 Chemical 4 \$14 Ingredient/lb of chemical A B C Chemical 1 0.03 0.02 0.01 Chemical 2 0.06 0.04 0.01 Chemical 3 0.10 0.03 0.04 Chemical 4 0.12 0.09 0.04 The Mist pharmacy produce four chemicals,

### System of non-homogenous first order differential equations

The volume of two tanks are V1 =100 gallons and V2 = 200 gallons .The inflow and outflow rates of the system are r = 10 gallons per minute. Suppose that the two tanks both contain fresh water initially, but the inflow to tank 1 is brine at 2 pounds per minute, so that 2 pounds of salt flow into tank 1 each minute. Write a matr

### Solve

Take a system of equations (make one up or use one of the exercises in the book, in chapter on systems of equations) and then solve it using THREE METHODS: substitution, elimination, and graphing. Please post before Sunday Midnight. I have attached the example.

### Applications of Linear Equations ...

Supply and demand at \$1.40 per bushel, the daily supply for oats is 850 bushels, and the daily demand is 580 bushels. When the price falls to \$1.20 per bushel, the daily supply decreases to 350 bushels and the daily demand increases to 980 bushels. Assume that the supply and demand equations are linear. Find the supply equat

### Linear Equations

Solve the system: {x+2y-z+2w+3t=11 {x-y+2z-w+2t=0 {2x+y-z+2w-t=4 {3x+2y-z+w-2t=2 {2x+y-z-2w+t=4

### Linear equations

I need help with the attached problems. 1.) Solve. 5/8x + 1/16x = 11/16 + x The solution is x=___. (Simplify answer. Type integer or fraction.) 2.) Solve. 8x - (6x + 4) = 6 The solution is x=____. 3.) Solve by the elimination method. 2x + 3y = 3 4x + 6y = 6 What is the solution of the system? _______ (Type an or

### Linear inequalities

Your friend is taking an algebra class that began one week after ours. Explain to your friend how to graph linear inequalities with two variables. Include at least two examples

### Mathematics - Algebra - Linear Equations Problem

Past history indicates that mutual fund A will earn 11.6% annually while mutual fund B will earn 9.8% annually. If an investment amount is divided between funds A and B so that the expected return will be 11%, how should the investment be split between the two funds?

### Mathematics - Algebra - Linear Equation Problems

Please help with the following linear algebra problem. It has been found that the percent of males in the workforce is constantly decreasing while the percentage of females is constantly increasing. The function m(t)= -.25t+85.4 where t= number of years since 1955, can be used to estimate the percent of males in the workfo

### Matlab for Lorenz equations with Gauss Seidel iteration

Hello I am taking a numerical methods class and I have limited Matlab skills to be able to complete this problem by myself. The problem is to linearize the Lorenz equations and then to write a Matlab program without using any built in Matlab solvers such as ODE45, etc. to create the Lorenz butterfly using linearized Lorenz

### Solutions of Linear Equations: One, No or Infinite Solution

Can you please assist me with the following problems. *Give examples (either a graph or the system of equations) of the 3 types of solutions to a system of linear equations - one solution, no solution, infinitely many solutions. *Why do absolute value equations usually have 2 solutions?

### Solving Systems of linear equations

Systems of linear equations Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for \$1.45,and June bought two books and five magazines for \$1.25. What was the price of a book and what was the price of a magazine? Solving

### Pair Solutions in System of Equations

Hello, I am learning algebra 2. I have no help and the textbook gives very few and vague examples. Can someone help me with my algebra 2 work. 1.Find all solutions for the following system of equations. List the solutions as ordered pairs. {x^2+y^2-25 = 0 2x-y = -5 2.Solve the system of linea

### Fibonacci Sequence - the matrix approach

The Fibonacci sequence is defined recursively as f_(n+1) = f_n + f_(n-1) . Obtain a closed form formulas for f_n using the iteration matrix (0,1,1,1) applied to the vector .. (see attached file). Consider a similar transform to diagonalize the iteration matrix.

II. You are planning on applying for a job with ABC Advertising. Many business decisions are based on unknown quantities, known as variables, encountered in business, economics, and social science. Thus, before the interview, you want to brush up on your knowledge of linear equations and linear inequalities. Complete the followi

### Linear equations and inequalities

1.Give 3 real-world examples where something is increasing at a constant rate or decreasing at a constant rate. The starting amount would be the y-intercept, "b", and the rate at which it increases would be the slope, "m". Give the equation of the lines for your examples using y = mx + b with your "m" and "b". 2. Why do we

### Systems of Equations: How to form the equations from a word problem.

1. How would you come up with the decimal point in this problem? 2. How does the author determine what the first equation should be? 3. What about the second equation? The second equation is the equation formed out of the second information in the problem, where the required mixture of the two components x and y is form

### Linear Equations: The Median Age of First Marriage

The median age at first marriage for females increased from 24.5 years in 1995 to 25.1 years in 2000 (U.S. Census Bureau, www.census.gov). Let 1995 be year 5 and 2000 be year 10. a.) Find the equation of the line through (5, 24.5) and (10, 25.1). b.) What do x and y represent in your equation? c.) Interpret the slope of

### Similarities and differences between functions & linear equations, difference between domain and range and Real-life Application of function

1. What similarities and differences do you see between functions and linear equations studied in chapter 3? A linear equation can have one, two, three or more variables and functions are expressed by using math symbols such as y is the output and x is the input. Are all linear equations functions? Yes, unless the functions eq

### Linear algebra

See attached Show that for a real symmetric matrix A=A^T, its singular values are exactly the absolute values of its eigenvalues.... Find the singular decomposition of... Verify the special theorem for the Hermitian matrix

### Solving System of Linear Equations/ Graphical Representation of Linear Equations - Solve ...

Solve by substitution or elimination method: 3x - 2y = 8 -12x + 8y = 32 2. Solve by substitution or elimination method: 7x - 5y = 14 -4x + y = 27 3. Solve by substitution or elimination method: -4x + 3y = 5 12x - 9y = -15 1. Plot the graph

### Round-off error and Matlab

Using MatLab, compute H^-1H for various n between 5 and 15. Describe the results and comment on the difference between the MatLab output and what is expected the answer to be (given that H is invertible for all n). At what point does Matlab give a warning indicating that it may not be giving the correct answer? Try using the

### Linear equation relating to every day life

create a system of linear equations from your own life, it can be an extension of previous work or something new entirely. 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

### Intermediate Algebra - 1. What similarities and differences do you see between functions and linear equations? ... 2. What is the difference between domain and ...

1. What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for someone to evaluate. 2. What is the difference be

### Gauss-Jordan elimination word problem

A particular diet calls for exactly 1000 units of vitamin A, exactly 1600 units of vitamin C, and exactly 2400 units of vitamin E. An individual is fed a mixture of three foods. Each gram of food 1 contains 2 units of vitamin A, 3 units of vitamin C, and 5 units of vitamin E. Each gram of food 2 contains 4 units of vitamin A, 7