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Linear Algebra

Proof of a Negative Real Number: Example Problem

For any two real numbers a and b, a < b if and only there exist a positive real number s such that a + s = b. Use this definition to prove that for any negative real number r, if a < b then a + r < b + r.

Solving Systems of Equations - Real World Example

There are many applications used in the area of solving systems of equations. For example, systems of equations can be used to find the optimal number of items to produce to ensure the highest profit of those particular items. Systems of equations can be solved by four methods: graphing, substitution, elimination or with matrice

Exports Linear Equation

Write a linear equation describing the number of exports each year with x=91 representing 1991 and x=101 representing 2001. In 1991, about 10 billion dollars of goods were exported to China. By 2001 this amount had grown to 19 billion dollars.

Linear equations with constants in denominators.

Step by step solutions to review problems. Linear equations with constants in denominators. Solve each equation. 18.) x/5 = x/6 +1 20.) x/5 - ½ = x/6 22.) x/2 = 3x/4 +5 24.) 2x - 2x/7 = x/2 + 17/2 26.) x + ¼ = 1/6 + 2-x/ 3 28.) 5 + x-2/ 3 + x + 3/8 30.) 3x/ 5 - x-3/ 2 = x+2/ 3

Linear Equations in One Variable

Solve and check the following linear equations: 1. 6x -3 = 63 2. 5x - (2x - 10) = 35 3. 3x + 5 = 2x + 13 4. 3x + 14 = 12x - 5 5. 2 (x - 1) + 3 = x - 3 (x + 1) 6. 2 - (7x + 5) = 13 - 3x 7. 5x - (2x + 2) = x + (3x - 5) 8. 45 - [4 - 2y - 4 (y + 7)] = -4 (1 + 3y - [4 - 3 (y + 2) - 2 (2y - 5)]

Linear Algebra Problem: Example

Find values of a, b and c ( if possible) such that the system of linear equations has (a) unique solution (b) no solution (c) an infinite number of solutions x+ y = 0 y + z= 0 x +z =0 ax+by+cz=0

The Initial Concentration of Pollutants in the Pond

Problem: An environmental group estimates that the amount of pollution in a pond will decrease by 10% each month. To determine the concentration C, of pollutants (in parts per million) after (m) months, the group uses the function C(m) = 23(0.95)m. (1) to the nearest tenth, what will be the concentration of pollutants in t

Mathematics - Systems of Linear Equations.

Determine if the following matrices are in reduced row echelon form. If it is not reduced, specify which criteria it fails to meet. a.[100|3] [001|2] [000|1] B.[100|3] [012|5] [001|6]

Matrix Algebra

1. Given the matrices [010] [100] [100] A=[101] B= 010] C=[000] [010] [001] [00-1] Show that A and B commute, B and C commute but A and C do not. 2. Show that the matrix [1 4 0] [2 5 0] [3 6 0] Is not invertible 3. Find the inv

Solve the Systems of Equations

5.Solve by substitution or elimination method: 3x - 2y = 26 -7x + 3y = -49 Solution: We'll use elimination method: Answer is (4,-7) 6.Solve by substitution or elimination method: 4x - 5y = 14 -12x + 15y = -42 Solution: We'll use elimination method: Ans

Graphical Representation of Linear Equations

Solve the questions on graphical representation of linear equations. Show all of your work and plot the graphs using the EZGraph tool. 1. Plot the graph of the equations 2x - 3y = 5 and 4x - 6y = 21 and interpret the result. 2. Plot the graph of the equations 4x - 6y = 12 and x - 5y = 10 and interpret the result. 3. Plot

Linear dependency of vectors

In the following case, state if the following set of vectors are linearly independent or linearly dependent. Justify your answer. G = {[(1, -1), (-1, 0)],[(1, -4), (1, 0)],[(1, -6), (1, 0)],[(0, 0), (1, 0)]} These are four 2x2 matrices

Algebra 3rd Set of Problems

Rossano, I need help with the followig exercises. I already finish all the exercises I just want to make sure they are done correctly. Thanks for your help. Exercises 1,2,3,4 Section 3.2: Exercise 64 Section 3.4: Exercises 80, 82, and 94 Section 7.1: Exercises 22, 24, 36, 38, 42, 56, and 70 Section 7.2: Exercises 8, 12, 16

Graphing and linear equations

Please see attached for the complete details of the given problems: WEEK HOMEWORK Please add explanation and colored fonts on your answers Page 483, #2 Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent. Page 483, #6 Solve by graphing. Indicate whether each system is inde

Problems on Linear Equations

1.Graph each line using y-intercept and slope. y+4x=8 2.in each case determine whether the lines are parallel,perpendicular,or neither. y=x+7 y=-x+2 3.the line is parallel to -3x+2y=9 and contains the point(-2,1) 4.Find the equation of each line in the form y=mx+b if possible. the line through(3,2) with undefined sl

Determine k for a linear system with infinite solutions.

Determine all values of k for which the given system has an infinite number of solutions: x1 + 2x1 + x3 = kx1 2x1 + x2 + x3 = kx2 x1 + x2 + 2x3 = kx3 I've figured that the determinant for the matrix in the system is -4. I just don't know how to use that to determine the solution of this problem. Please help. Thanks.

Linear equation problems

1. Find an equation of the line with the given slope and containing the given point. m =2/3, (8,7) a. y = (2/3)x + 8 b. y = 2/3)x + 8 c. y = 5/3 d. y = (2/3)x + 5/3 2. Graph the linear inequality x + y less than = _6

Systems of equations.

Solve this system of equation. 1. y - 5x = 4 6y = 30x + 24 a. (1,1) b. there are an infinite number of solutions. c. There is no solution d. (-1.5, -1) 2. The length of the garden is 7 feet more than 5 times the width. I need 86 feet of fencing to do the job. How many feet is the LENGTH of the gard

Linear equations

1. Complete the ordered pair so it is a solution to the given linear equation. give the answer as an ordered pair using parentheses and a comma. 3x + y = -7 (,2 2. solve these 2 system of equations x - y = -5 x + 4y = 15 5x + y = 0 -5x + y = -10 3. Find the slope, if possible of the line passing through the pair

Matching graphs to a function.

1. Ture or false: The ordered pair (-1, 4) is a solution to the linear inequality: -5x + 2y < = 13 2. We know that y varies directly with x, and y = 1.5 when x = 0.3. Write the linear equation relating the two variables in slope-intercept form. 3. choose the graph of the function f(x) = x^2 - 8x + 16

Discussion Board Exploring Systems of Equations & Inequalies

Programmers need to solve systems of equations, which often come up during the design of the games. As an example, suppose in a video game two persons (or objects) are traveling along linear paths,and we need to find the coordinates where they might potentially collide. Suppose the two lines are 2x + 3y = 8 and 4x - y = -2. solv

Apply Separation of Variables to the PDE to get 2 ODE's

I have included a Wave Equation problem with parts a-c, that has variable tension. It involves separation of variables, the Sturm-Liouville system, and an application to the "Rayleigh Quotient" involving the Eigenvalues. I have included notes on the Sturm-Liouville system with examples and properties. Please refer to these notes

Algebra: Solving and graphing systems of equations

I have a few questions I need help with. What are the steps to solving a system of equation by elimination? What are the steps to solving a system of equation by substitution? What are the steps to solving a system of equation by graphing? Once you have graph a system of equation, how do you check your answer? Whe

Equations

Provide Details using addition/elimination.....Strategy for the addition Method. 3x+5y=-11 x-2y=11 Solving each system by substitution or addition 2x-x=3 x=3y-5 solve by substitution, indicate, independent, dependent, or inconsistent 3y=x+5 3x-9y=-10 solve by addition, Indicate, independent, dependent, or inconsi

Methods of Solving Systems of Equations

When solving a system of equations, what are the 3 possible outcomes? Describe how you can determine each of the possible outcomes using one of the algebraic methods. Do not look at the graph. Do not look at the individual equations, just look at the outcome, the "answer" you get after using substitution or elimination/a

Systems of Equations

Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the

Real-Life Application of a Linear Equation

Linear equations provide information on how quickly data is rising or falling, known as the slope of the equation. Find a real-world application of a linear equation and discuss the meaning of the equation. Explain how the values of the slope affect the overall meaning of the equation.