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# Linear Algebra

### 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.

### Prove that Binomial[2n, n] = Sum from k=0 to n of Binomial[n,k]^2

Prove that (2n choose n) = the sum from k=0 to n of (n choose k) squared.

### Algebra

Sue is offered a new job selling furniture where she makes a base pay of \$1500 a month plus commission. According to a current employee, she should be able to earn \$30,000 in sales monthly. To maintain her standard of living she must make \$3000 total monthly. What commission rate must she earn to maintain her standard of livi

### Functions and Linear Equations

Could you explain to me the difference between functions and linear equations? I need to know if all linear equations are functions and if there are any instances in which a linear equation is not a function. Could you create an equation of a non linear function and provide 2 inputs so they can be evaluated? also Could you e

### Inconsistent or dependent system of equations

Solve the system of linear equations. If the unique solution does not exist state weather the system is inconsistent or dependent. 1. -x - y = 4 x -y = -8 2. 3x - 2y = 23 x +5y = -15 3. 4x + 2y = 4 y = 2 - 2x 4. 4x - 3y = 9 2x + y = 12 5. 5x + 4y = 40 x + 2y = 11

### Probability, Linear Programming and Statistics

Show your work. 1. (3 points) Find the equation of the line shown: 2. (6 points) A bank loaned \$15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was \$1800, how much was loaned at 10%? 3. (3 point) Write the augmented matrix of the system: 2x1 -3x2 +

### Systems of Equations with Three Variables

Given &#928;0 = 0.5&#928;0 + 0.3&#928;1 +0.2 &#928;2 &#928;1 = 0.4&#928;0 + 0.4&#928;1 + 0.3&#928;2 &#928;2 = 0.1&#928;0 + 0.3&#928;1 + 0.5&#928;2 Where 1 = &#928;0 + &#928;1 + &#928;2 The solution should yield: &#928;0 = 21/62 &#928;1 = 23/62 &#928;2 = 18/62 Please see the attached file for the fully formatted

### Graphing Equations and Inequalities

Plot (- 1, 4) on the coordinate axes; I cannot insert the letter X which belongs on the side of the graph just like the letter Y is above. Y The numbers are 1through 10; also a negative 1-10;

### Linear Equation Word Problems

Please see the attached file for the fully formatted problems. 1. Translate the sentence to an equation and solve it. Six less than eight times a number is equal to that number added to one. 2. The length of a rectangular mailing label is 3 centimeters less than twice the width. The perimeter is 54 centimeters. Find the d

### System of differential equations

Please see the attached file for the fully formatted problems. consider the following system: dX/dt = AX + B Where A= (1 4) (0 2) And B = (3,6) a. Determine the equilibrium point X* of the system. b. Is the equilibrium point stable or unstable? c. Draw precisely the phase portrait of the system.

### Exponential Functions : Population Growth

The U.S. Census Bureau International Database gives the population of the ten most- populated countries in the year 2000 and population predictions for 2050 for these countries: Chinahad 1.2 billion people in 2000 and is predicted to have a population of 1.3 billion in 2050. The U.S. had a population of 284 million in 2000 with

### Semidirect product or split extention

If H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H. If sigma=(12) in S_n, n>=2, show that s_n is a semidirect product of A_n by <sigma> Show that the dihedral group D_n=<a,b|a^n=b^2=1,b^-1ab=a^-1> is a semidirect produc

### Calculations for solving systems of equations

Please help with the following problems. Provide step by step calculations. 3. Solve for X, Y, and Z in the following systems of three equations: a. X + 2Y + Z = 6 X + Y = 4 3X + Y + Z = 8 b. 10X + Y + Z = 12 8X + 2Y +Z = 11 20X - 10Y - 2Z = 8 c. 22X + 5Y + 7Z = 12 10X + 3Y + 2Z = 5

### Linear Equations: Slopes and Intercepts

PLEASE SEE ATTACHED FILE FOR FULLY FORMATTED QUESTIONS 1. Find the slope of the line. ANSWER: 2. Find the slope of the line that goes through the pair of points: (2, 5), (6, 10). 3. Graph the line through (2, 3) with slope . 4. Draw L1 through (-2, 1) with slope , and draw L2 through (-2, 1) with sl

### Solving equations and system of equations

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 anno

### Algebra - Linear equations.

Please explain and answer questions. Thanks 1. Equations of Lines in Slope-Intercept Form Find the slope and y-intercept for each line. 3x + 5y + 10 = 0 2. Write each equation in slope-intercept form y- 5 = - ¾ (x+1) 3. Interest rates. A credit manager rates each applicant for a car loan on a scale of

### Linear Equations

Please help with the following problems. There are three methods to solving Linear Systems with two Equations. They are the Graph method, the Elimination method, and the Substitution method. When would you use each method? What makes each method better than the other methods?

### Systems of Equations Application Word Problems

1-2 pages Details: 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

### Solving Systems of Linear Equations and Word Problems

1.) Solving Systems by Graphing and Substitution Investing her bonus. Donna invested her \$33,000 bonus and received a total of \$970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? 2.) Ticket sa

### 1 page plus graph as attachment---Solve equations and systems of equations in two variables, formulate real-world problems in terms of linear equations and solve these systems by several commonly applied methods.

The financial institution was very pleased with your presentation and has asked you to place the advertising ads. You have found out the best way to ensure the best outcome for your customer is through the use of systems of equations. After reading up on systems of equations, you have found out how powerful they can be for solvi

### Linear Equations, Linear Programming, Word Problems and Measures of Central Tendency

Show your work. 1. (3 points) Find the equation of the line shown: 2. (6 points) A bank loaned \$15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was \$1800, how much was loaned at 10%? 3. (3 point) Write the augmented matrix of the system: 2x1 -3x2 + x3 =

### Solving Systems of Linear Equations

Solve each step by graphing y = -2/3x 2x+3y = 5 Answer: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent x= y + 3 3x - 2y =4 Answer: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent 2x -

### Graphing Linear Equations

Please see the attached file for the fully formatted problems. 1. a) Determine if the ordered pair (2, ¼) is a solution of the equation (1/8)x + 3y = 1 b) Explain why or why not the pair is a solution. 2. a)Graph or describe fully the graph of the equation y = (2/3)x + 1. b) Show the table method with values for x o

### Basic Algebra : Mean, Median, Mode and Linear Equations

Fiona kept the following records of her phone bills for 12 months: \$42, \$37, \$51, \$41, \$58, \$44, \$42, \$35, \$53, \$58, \$46, \$57 Find the median of Fiona's monthly phone bills. (a) Find the mean of the following set of numbers. 12, 16, 19, 22, 28, 30 (b) Find the mode of the following set of numbers. 11, 1