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# Linear Algebra

### Equations and inequalities

Solve the system by the substitution method 6x+5y=10 -4x+y=28 Solve the system by the elimination method 5x+5y=-11 7x-3y= 19 Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent. 3x-9y=63 2x-6y= -8

### Matrix Theory Functions

Please see the attached file. Thank-you for your help. Let B = . Find each of the following. You may use a calculator to replace hand calculation for row reduction and finding the characteristic polynomial. Show your work; don't just write down the answers. (a) Find the characteristic polynomial of "A". (b) Find the

### Mathematics - Algebra - Linear Equations for Selling Shirts

86. Selling shirts. If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000 -100p shirts at a tournament a) Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each. b) Find R(5), R(10), and R(20). c) Use the bar graph to determine the price that will give the

### Explain matrices Deliverable Length: 2-4 paragraphs plus graphs

Deliverable Length: 2-4 paragraphs plus graphs Details: 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.

### Linear Programming Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bound or unbounded.

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bound or unbounded. 22. x + y > -2 3x - y < 6 26. 4x - 3y < 12 5x + 2y < 10 x > 0, y > 0 30. 3x + 4y > 12 2x - y > -2 0 < y < 3 x > 0 Formulate each of the following

### Equations

See attached for full description. 4. Decide whether the pair of lines is parallel, perpendicular, or neither. 4x+5y=5 5x+4y=7 8. Solve for x. 8x-(5x+7)=14 10. Simplify. -3[87-(-55-35)] 14. Find the domain of the function. p(x) = x^2 -2x + 7 23. Solve using the substitution method. 6x+7

### Equation has infinitely many solutions 50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

### eigenvalue and eigenvector of matrix

Please see attached file for full description. Show that v is an eigenvector of A and find the corresponding eigenvalue. Show that lamda is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue. 8. A = [ 2 2, 2 -1], lamda = -2 10. A = [0 4, -1 5]; lamda = 4 Use the method of Example 4.5 to find

### System of linear equations and algebra word problems

Need assistance on problemsProblems needing assistance 1. What is the solution of the system? Type an ordered pair 5x+3y= -11 7x-2y= 17 2. Hockey team receives 2 points when they win and 1 point when they tie. One season, a team won a championship with 60 points. They won 12 more games than they tied. How many wins and h

### Linear Problem - According to http://www.whitehouse.gov/omb/budget/fy2006/tables.html, the U.S. government received approximately \$2 trillion in funds during the year 2005. Approximately \$1.3 trillion had already been promised to programs such as Medicare and Social Security, leaving approximately \$700 billion in "discretionary" funds for budget items like defense and education. ...

According to http://www.whitehouse.gov/omb/budget/fy2006/tables.html, the U.S. government received approximately \$2 trillion in funds during the year 2005. Approximately \$1.3 trillion had already been promised to programs such as Medicare and Social Security, leaving approximately \$700 billion in "discretionary" funds for budget

### Word problem on linear equations

The credit remaining on a phone card is a linear function of the total calling time. The function gives a line with a slope of -.32, when graphed. There is \$62.05 in credit remaining after 70 minutes of calls. What is the credit outstanding after 53 minutes?

### Algebra - Linear Equations Certain Race

1. In 1920 the record for a certain race was 46.7 sec. In 1980, it was 46.1 sec. Let R(t)= the record in the race and t= the number of years since 1920. a. Find a linear function that fits the data b. Use the function in (a) to predict the record in 2003 and in 2006 c. Find the year when the record will be 45.8 sec 2 I

### Linear equations and graphs

Need help with attached problems. Problems I need help with 1. Find an equation of the line containing the given pair of points. Express your answer in the form x=a, y=b or y=mx+b (-4,-4) and (3,3) What is an equation of the line y= 2. Find an equation of the line having the given slope and containing the given p

### How long was each storm

Two rainstorms occurred in one week in a certain area. In the first storm 35 mL of rain fell per hour, and the second storm 40 mL of rain fell per hour. Rain fell that week for a total of 70 hours for a total rainfall of 2650mL. How long was each storm?

### Using Linear Regression Method to Find Estimated Sales Equation

1. Consider the following annual sales data for 1996-2003, use the linear regression method and determine the estimated sales equation. Year Sales 1996 2 1997 4 1998 10 1999 8 2000 14 2001 18 2002 17 2003 20 2. Solve the

### Methods of solving

Write one or two paragraphs comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by providing appropriate examples.

### Methods of solving - Write one or two paragraphs comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by providing appropriate examples.

Write one or two paragraphs comparing and contrasting all methods of solving systems of linear equations with two variables. Explain which method you prefer and why. Support your answer by providing appropriate examples.

### Explanation of Regression Analysis and Equation

Given the following data: Height (in) 71 70.5 71 72 70 70 66.5 70 71 Weight (lbs) 125 119 128 128 119 127 105 123 115 Find the best predicted weight of a supermodel that is 69 inches tall.

### Linear regression

Given the following data: Height 71 70.5 71 72 70 70 66.5 70 71 (in) Weight 125 119 128 128 119 127 105 123 115 (lbs) Find the value of the y-intercept of the linear regression equation.

### Maximize profit - Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are

24. Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next three months. Each table will require 30 hours of labor, each will require 18 hour

### Several Problems on Linear Equations and System of Equations

1. Graph the equation using the slope and the y-intercept,Y= 7/5x+5 2. Solve, -0.6x < -30 3. Graph the equation of y+ x =10 and identify the y-intercept 4. Graph the system of inequalities ; y ≥ -1 and x ≥ 6 5. Solve, -6x > 1/13 6. Solve, -8 ≤ 4x -7 ≤ 2 7. Solve, the length of a rectangle is fixed at 30cm. What wid

### Algebra - Solving a Linear Programming Problem

1. Find the complete (including values for slack variables) optimal solution to this linear programming problem using. graphical method Min 5X + 6Y s.t. 3X + Y > 15 X + 2Y > 12 3X + 2Y > 24 X , Y > 0 2. Find the complete (including values for slack variables) optimal solution

### Several problems on system of linear equations

1. Solve the system by addition or substitution. -9x - 3y = 22 y = -3x - 6 2. A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60

### 1. What are the different forms of linear equations in two variables? Show an example of each form. 2. How does the sign or value of the slope determine its type (i.e. whether it is +ve, -ve, undefined, or zero)? And how do you interpret the relationship between two variables (independent and dependent) based on the type of the slope?

1. What are the different forms of linear equations in two variables? Show an example of each form. 2. How does the sign or value of the slope determine its type (i.e. whether it is +ve, -ve, undefined, or zero)? And how do you interpret the relationship between two variables (independent and dependent) based on the typ

### Several problems on linear/quadratic equations

1A: Applications of Linear Equations Solve the following questions and submit your response to the W4: Assignment 1 Dropbox. 1. Joe has a collection of nickels and dimes that is worth \$5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be \$10.45. How many dim

### Depreciation - 1. Jackie buys a computer for \$3600. For tax purposes, she declares a linear depreciation (loss of value) of \$600 per year. Let y be the declared value of the computer after x years. If the linear relation of the depreciation model in this situation is given by 3600 - y = 600x

1. Jackie buys a computer for \$3600. For tax purposes, she declares a linear depreciation (loss of value) of \$600 per year. Let y be the declared value of the computer after x years. If the linear relation of the depreciation model in this situation is given by 3600 - y = 600x a. What is the slope of the line that m

### Important information about Algebra - Linear Programming

11.Irwin Textile Mills produces two types of cotton cloth denim and corduroy. corduroy is a heavier grade of cotton cloth and as such requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. a yard of corduroy requires 3.2 hrs of processing time;a yard of denim requires 3.0 hrs. althoug

### Normal Equations and Projection Matrices

1. consider the following subspaces of R^4 V=span{v1,v2,v3}, W=span{w1,w2,w3} where v1=(1,2,1,-2)^T w1=(1,1,1,1)^T v2=(2,3,1,0)^T w2=(1,0,1,-1)^T v3=(1,2,2,-3)^T w3=(1,3,0,-4)^T a)Find two systems of homogeneous linear equations whose solution spaces are V and W, respectively. b)Find a basis f

### Difference - One fundamental difference between a linear equation and a linear inequality lies in the number of possible solutions. A linear equation has a finite (limited) number of solutions while the linear inequality has a range (set) of solutions.

One fundamental difference between a linear equation and a linear inequality lies in the number of possible solutions. A linear equation has a finite (limited) number of solutions while the linear inequality has a range (set) of solutions. I need an example of an equation and an inequality that expresses the above difference

### Linear algebraic equations

Problems 1. How are addition and multiplication used to solve a linear equation? Demonstrate by solving "15x + 7 = 31 + 3x" 2. Translate the following into a system of equations, then solve it:A customer walks into an electronics store and buys five MP3 players and eight sets of headphones, paying \$840. A second customer