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# Linear Algebra

### Graphing Linear Equations and Applications

The number of arrests y of a city over a period of time x is graphed on a rectangular coordinate system. Write a paragraph describing your interpretation when the slope is positive, zero, and negative. If you were buying a home in this particular city, which slope would be most attractive to you and why?

### Discussing Functions and Linear Equations

Hi, I need some assistance computing the following mathematical questions so that I can create a study guide. Answer the following questions and if required, do calculations to please show your work: 1. What is a function? 2. What is a linear function? 3. What form does a linear function take? (e.e., What is the

### System of inequalities, Applicable corner point, Maximize profit

1. A company makes two soft drinks A and B. Each liter of A requires 4 hours processing and 4 hours distillation while each liter of B requires 5 hours processing and 3 hours distillation. The capacity of the factory is limited to 160 hours processing time and 120 hours distillation time. Profits from product A are \$7 and from p

### Eigenvalue and Eigenvector Pair

1. Solve the system -16 12 -18 14 with the initial value -3 -6 . . 2. Solve the system -8 0 -4 0 with the initial value -16 -9 . . 3. Solve the system 4 -1 1 4

### Matrix determinant, Cramer's rule, Gaussian elimination

1). Write the matrix in reduced row-echelon form: [1, 2, -1, 3], [7, -1, 0, 2], [3, 2, 1,-1]. 2) Find the equation of the parabola that passes through the given points. Use the graphing utility to verify your result. (Please look at the picture). 3) Use a graphing utility to find AB, given. A= [1, 3, 6], [4, 1, 3] B= [0, 1

### Demand equation. Helen's Health Foods usually sells

Please answer the enclosed 6 questions and use EXCEL for graphs. Please answer the following questions....all graphs must be done in EXCEL. Question#1 Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is \$5 per can. After experimenting with prices for some time

### Linear equations in business

Why is it important to understand linear equations in business? In particular can you provide examples where the relationship between items that can be affected by management and 'items' that management wished to achieve or attain may be 'linear'? Can you think of items for which the relationship is NOT linear?

### Solve each system by the elimination method.

Solve each system by the elimination method. Check each solution. See Examples 1 and 2. 1. x + y = 2 3. 2x + y = -5 5. 3x + 2y = 0 2x - y = -5 x - y = 2 -3x - y = 3 2. 3x - y = -12 4. 2x + y = -15 6 . 5x - y = 5

### Problems with Systems of Linear Equations

A company has an income of \$100,000 before paying taxes and a bonus. The bonus (B) is to be 20% of the income after deducting income taxes (T) but before deducting the bonus. So B = 0.20(100,000 - T ). Because the bonus is a deductible expense, the amount of income tax (T) at a 40% rate is 40% of the income after deducti

### How do you solve linear equations?

1. What is a system of equations? 2. Solve for X and Y in the following problems. Show all your work. a. X + Y= 10 , 3X + Y = 12 b. 2X + 5Y = 19 , 3X + 3Y = 15 c. 4X + Y = 22 , 2X + 3Y = 16 d. 12X + Y = 174 , 8X - 2Y = 36 3. Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y

### This is a multi-question problem that involves a) graphing a straight line given two points, b) graphing two straight lines to find the solution, c) finding the x- and y-intercepts given the equation, d) writing the equation of a linear given the slope and a point, e) solving problems that have two variables, f) finding the equation of a line given two points.

1. Find the values of x and y that solve the following system of equation -5x - 7y = 12 9x - 5y = -4 2. The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers? 3. Find an equation of the line that is parallel to the line y = 2x - 5 and that passes through the point (8,2)

### System of Equations: Example

1. find the values of x and y that solve the following system of equations. -5x + 4y = -13 8x - 9y = 0 2. The sum of two numbers is 40. One number is 4 times as larger as the other. What are the numbers 3. A motorboat travels 639 miles in 9 hrs going upstream and 833 miles in 7 hrs going downstream. What is the rate of t

### Sytems of linear equations using 2 variables

Solve by substitution, indicate whether each system is independent, dependent, or inconsistent. 3y = x + 5 3x - 9y = -10 Solve by addition, indicate whether each system is independent, dependent, or inconsistent -3x + y = 3 2x - 3y = 5

### Systems of linear equations using 2 variables.

Equations involving fractions or decimals, solve using the addition method 1. 3/7x + 5/9y = 27 1/9x + 2/7y = 7 2. 3x -2.5y = 7.125 2.5x - 3y = 7.3125 3. solve by graphing. Indicate whether each system is: independent, dependent, inconsistent y = 3x - 4 y = 2x + 1 3x - y = 4 3x - y = 0

### System of Linear Equations with 2 Variables

1. Solve by graphing 3y - 3x = 9 x - y = 1 2. solve by substitution and determine whether equations are independent, dependent, or inconsistent 7y = 9x -3x = 4y 3. solve by substitution method x + 6y = -2 5x - 20y = 5.

### Simultaneous Linear Equations in Two Variables

A landscaper wants to combine golden landscape rock with rust-colored landscape rock to make a mix. The golden rock costs \$0.59 per pound and the rust-colored rock cost \$0.49 per pound. If the landscaper buys 70 pounds of the mixture costing a total of \$38.80, how much of the rust-colored rock did he buy? ___Pounds

### Calculation of Roots of a System of Linear Equations

Please advise. My son is preparing for his jr. high algebra I finals and he is having problems with the following problems: solve using addition or subtraction elimination. -3y + 4y = 15 3x + 6y = 5 solve using multiplication elimination 4x - y = 12 -3 + y = 6.

### Substitution and elimination methods

Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.

### Linear Equation, Slope and Intercepts

1. Solving for two points of a linear equation gives you the same graph for the line represented by the equation. Can you give any examples of where solving a linear equation is useful in any of our daily activities? 2. Determining the slope and y intercept is very important in graphing a solution. How would you relate slop

### Systems of Linear Equations & Inequalities

1) For the equations, you are learning several methods of finding the solution to a system. Is there a difference in the result you get using an algebraic method and what you get using a graphical method? Why or why not? How does the graph of two linear equations relate to the number of solutions to the system? How could you

### Equilibrium Values in Systems of Difference Equations

Consider the interaction of two species whose populations after n years are represented by the numbers xn and yn. Consider the following model: xn+1 = 0.8xn + 0.002xnyn yn+1 = 0.9yn + 0.001xnyn x0 = 50 y0 = 100 Iterate the system. Can the two species coexist? Is there an equilibrium value?

### Algebra

1. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. 5x - 2y = -1 x + 4y = 35 2. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -4x + 9y = 20 -2x - 2y = 10

### Linear equations and linear systems

1. Find the intercept, then graph in a document. Y = -40 + 5x 2. On February 10th, Oscar rented a Chevy Trailblazer with a full tank of gas and 13,091 miles on the odometer. On February 12th he returned the vehicle with 13,322 on the odometer. The rental agency charged \$92.00 and needed 14 gallons of gas to fill the tan

### Solving a word problem using a system of linear equations

I'm just drawing a blank on how to work this type of problem and I have several of this type.Could you please explain step by step how to solve this type of algebra problem please? Word problem--- The combined cost of one advance ticket and one same-day ticket to a show was \$45. It is known that 30 tickets were sold in adv

### Show that a group is not simple

Let G be a group so that |G|=p^2q^n, for p, q primes with q > p >=3. Show that G is not simple. Hint: Look at the q-Sylow subgroups. There cannot be p of them so what happens if there are P2 of them?

### MAT101 - College Mathematics (Systems & Equations)

For this SLP I want you to create a system of linear equations from your own life, it can be an extension of your module 2 SLP 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.,

### matrix that does not have a determinant

Please help me with the quetions below. Thank you. Do all matrices have a determinant? Why or why not? Provide an example of a matrix that does not have a determinant. Do all matrices have an inverse? Why or why not? Provide an example of a matrix that does not have an inverse.

### Solving Linear System of Equations by Matrix Method

Use Row Reduction and Back Substitution to solve the given Linear System of Equations. Write the Augmented Matrix for each of them. [Please refer to the attachment for the given linear system of equations].

### Linear Algebra: Quadratic Polynomials and Complex Coefficients

Question Details: a) Write the expression in the form a+bi for a,b,in R. &#945;=5 b) Solve quadratic equation 2x2 + ( 2+10i ) x + (-4 + 5i ) = 0 Simplify as much as possible. Hint: The formula for the roots of a quadratic polynomial also holds for quadratic polynomials with complex coefficients.

### Population with Linear Growth Model: Example Problem

Rate of Growth is: 300 a) Use your equation in part b(equations: P = 300t + 1750) to approximate how many years it will take the population to reach 7000. b) Graph this function in MS Excel by plotting the points found in your chart in part a. Label your axes with time on the x-axis and population on the y-axis.