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# Linear Algebra

### Detailed Explanation to Linear equations

Answer following questions showing your work for all problems. Part I Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X2 b. (X-1)2 + (Y-8)2 = 16 c. (X+2)2 + (Y-4)2 =

### Converting linear equations to slope-intercept form

Write the two equations in slope-intercept form, and then determine how many solutions the system has. x - 3y = 6 3y + 1 = x

### Algebra: Linear Equations and Inequalities

1. The surface area S of a right prism is given by S = 2B + Ph. B is the area of the base. P is the perimeter of the base. And h is the height of the prism. Solve for B. 2. The length of a rectangle is five times its width. If the area of the rectangle is 500m², find its perimeter. 3. The sum of two numbers is grea

### Eigenvalues of Matrix

Find all eigenvalues of a matrix (see attached document). - For each eigenvalue find a basis of the corresponding eigenspace. - Decide if A is diagonalizable or not. If yes, give an invertible matrix P and a diagonal matrix D such that P-1AP = D. Justify the answer.

### Polynomial of degree 3 - Linear Algebra

Find a polynomial p of degree 3 satisfying: p(-2)=49, p(-1)=10, p(1)= -2, p(2)= -23

### Algebra: Linear Equations

1 The sum of two numbers os 41. One number 3 times as large as the other. What are the numbers? 2 In a family there are two cars. In a given week, the car gets an average of 20 miles per gallon, and the second car gets 25 miles per gallon. The two cars combined drive a total of 1025 miles in that week, for a total gas a tota

### Solving linear transformation problems

For each of the following functions decide whether or not the function is a linear transformation. Prove your answer in each case: (a) F: V3(R) --> V2(R) defined by F(a1, a2, a3) = (2a1 - a2, 3a3) (b) G: V3(R) --> V2(R) defined by G(a1, a2, a3) = (a1 - a2 + a3, a1 + a2a3)

### Inequality and Linear Equation in One Variable

1. Solve using the five-step problem-solving process. Don't forget to include the fifth check equation step of the problem- solving process in your answer. The difference between two positive integers is 36. One integer is three times as great as the other. Find the integers. 2. Use an inequality and the five step problem-so

### Write a system of two equations in two unknowns

Write a system of two equations in two unknowns for each problem. Solve each system by substitution. Free market. The equations S=5000+200x and D=9500-100x express the supply S and the demand D, respectively, for a popular compact disc brand in terms of its price x (in dollars). What happens to the supply as the price in

### 55 Problems on Algebraic Equations and Graphs

2. Use the intercepts to graph the equation. X + 3y = 6 then graph 3. Solve. Then graph Y -5 > -14 The solution is {y|y>__} A. -11 -10 -9) -8 -7 B. -11 -10 (-9 -8 -7 C. -11 -10 [-9 -8 -7 D. -11 -10 -9] -8 -7 4. Multiply -5/8 x (-5/8) =__ 5. Determine whether (7,-2)

### Linear 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.,

### System of equations

1. What is a system of equations? 2. Solve for X and Y in the following problems using either substitution or elimination methods. Make sure you show all your work so you can get partial credit even if your final answer is wrong. a. X + Y = 10 , 3X + Y = 12 b. 2X + 5Y = 19 , 3X + 3Y = 15 c. 4X + Y = 22 ,

### Linear Equations and Inequalities

Part 1: Using the Library, web resources, and/or other materials, find a record-breaking temperature (in degrees Fahrenheit) for a town or city of your choice. Include the name of the town, along with the temperature, and what record was broken. Give the formula for converting degrees Fahrenheit to degrees Celsius. Using the for

### Appendix F - Buying A House

For most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also a commitment. Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. C

### Three Algebra Word Problems on Simultaneous Linear Equations

1. 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? 2. Ziggy's Famous Yogurt blends regular yogurt that is 3%

### Linear Trendline, Trend Equation and Forecast

See data file attached. (a) Plot the data on fruit and vegetable consumption. (b) Discuss the underlying causes that might explain the trend or pattern. (c) Fit a linear trend to the data. (d) Interpret the trend equation. What are its implications for producers? (e) Make a forecast for 2005. Note: Time increments ar

### Polynomials, Fractions, Linear Equations, Simultaneous Linear Equations, Word Problems, Graphs, Slope and Intercept of Lines

Please refer to the attachment. Build up the following fraction so that it is equivalent to the fraction on the left hand side of the equation. Perform the indicated operations without using a calculator.  -10 - 18 =  -1 + (-20) = Determine if x = 2 is a solution to the following equation Simp

### Instances One Would use a Non-Linear or Linear Description

What are some instances in which one have used (or could use) a non-linear description? What are some instances in which one have encountered, in which you have used (or could use) a linear description?

### Mathematics: Union, Intersection, and Complements

1. Match the word and definition or symbol. ____ A. Union 1. {} ____ B. Intersection 2. A' U B' ____ C. Complement 3. ' ____ D. Empty Set 4. A' &#8745; B' ____ E. (A &#8745; B)' 5. &#8745; ____ F. (A U B)' 6. U 2. Two sets are disjoint if their intersection is a null set. If set A = {1,2,3,4,5,6}, se

### Eigenvalues must be zero

Please refer to the attached file. Assume that T and U are linear operators on R^3, that UT = -TU and that UT has three distinct eigenvalues. Prove that one of the eigenvalues must be zero. (Hint: do the proof by contradiction: Assume the hypotheses and assume that none of the eigenvalues are zero. UT is one to one and there

### For the systems of linear equations in questions 1-3

Week 3 Assignment 3: Mixed Problems For the systems of linear equations in questions 1-3 - Determine how many solutions exist - Use either elimination or substitution to find the solutions (if any) - Graph the two lines, labeling the x-intercepts, y-intercepts, and points of intersection 1. (8 points) y = 2x + 3 an

### linear system of two unknowns

Let A = [1 2 -3 5] Let X = [x1 x2] Let B = [-4 12] Show that the equation AX = B represents a linear system of two equations in two unknowns Solve the system and substitute into the matrix equation to check your results

### linear equation and inequalities in one variable

1. 2. 6u+ 3. w + 10>13 4. 3z + 1 < -14 5. -5w-9 6. Customers of a phone company can choose between two service plans for long distance calls. The first plan has a one-time activation fee and charges cents a minute. The second plan has no activation fee and charges cents a minute. After how man

### Determining a System of Linear Equations

1. Emily Harrington made two investments for one year totaling \$7,000. The interest rates were 4% and 7%. If she received \$415 in interest, how much money was invested at each rate? at 4% at 7% 2. Two lengths of wire total 132 fest. One length is 42 feet longer than the other. How long is each length of the wire? And 3.

### Using the Library, web resources, and/or other materials, find a record-breaking temperature (in degrees Fahrenheit) for a town or city of your choice.

Part 1: Using the Library, web resources, and/or other materials, find a record-breaking temperature (in degrees Fahrenheit) for a town or city of your choice. Include the name of the town, along with the temperature, and what record was broken. Give the formula for converting degrees Fahrenheit to degrees Celsius. Using the for

### Linear Algebra Problems on Echelon Method

1) Use the echelon method to solve the system of two equations in two unknowns. 9x+8y=72 -6x-3y=-48 Solve the problem. 2) Linda invests \$25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is \$1600. The income from the 5% and 6% investments is the sam

### Algebra - Linear Equation for a School Library

Solve the problem 5). A school library has \$15,000 to spend on new books among the four categories of biology, chemistry, physics, and mathematics. If the amount spent on biology books is to be the same as the amount spent on chemistry books and if the amount spent on mathematics books is to be the same as the total spent

### Essay problem using conic sections and non-linear systems

I'm offering a lot of credits for this assignment because I really need help - and I am asking for more than just solving a problem. So please don't take this assignment if you can't help with everything I need. I have worked on this problem but I'm not certain it is correct (it seemed to easy and I'm not seeing where conic

### Graphing linear equations, word problems.

1. Graph this equation. y = 3/2x +1 2. Determine whether each pair of equations represents parallel lines. y = -5/4 +1, y = 5/4x +3 4. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. x + 8y = 8 9x - 5y = -5

### Systems of Equations and interpretation of graphical data

The bar graph shows the percentage of Americans who used cigarettes, by ethnicity, in 1985 and 2002. For each of the groups shown, cigarette use has been linearly decreasing. Use this information to solve exercise 72. *GRAPH IS IN ATTACHMENT* 72) In this exercise, let x represent the number of years after 1985 and let y r