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# Linear Algebra

### Linear Equations In Real World

I need to show a linear equation and explain what it represents. I need to state what the "x" and "Y" in equation represents I have to be able to evaluate the equation for at least two variables and provide reference where you got the equation from. Part 2: Using the Library, web resources, and/or other materials, find a r

### Judy and Pete are building a new house and want to carpet their living room

Please see the attached file. 1. Judy and Pete are building a new house and want to carpet their living room, except for the entrance way and the semicircle in front of the fireplace that they want to tile (Alexander & Koeberlein, 2003). A. How many square yards of carpeting are needed? (Hint: There are 9 square feet

### Several problems on quadratic function & system of equations Fran swims at a speed of 2.4km/h in still water.

1. 2x-9=-3 The solution is x= 2. Fran swims at a speed of 2.4km/h in still water. The lazy river flows at a speed of 0.8km/h. How long will it take Fran to swim 1.6km upstream. It will take Fran ____ hr to swim 1.6 km upstream 3. |x-6|=27 The solution set is ? 4. g(x)=10/1-2x What is the correct domain 5.

### A stamp collection consists of 3, 8, and 15 cent stamps.

A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is \$2.47. Find the number of 8 cent stamps in the collection?

### Determinants, Matrices, Inverse, Linear equations

Practice problems on determinants and matrices. All questions can be found in the attached file. Write the matrix equation as a system of equations and solve the system. ■(1&2&3@1&1&1@-1&1&2) {█(x@y@z)┤ = {█(1@12@2)┤ Find the determinant of the given matrix. ■(1&0&6 -1@-6&0&2 4@3&0&6 -2 )

### Landscape Design, Buying a Home and Fueling up

Questions 1. Exercise: Four Concept Check Post your 50 word response to the following: Explain in your own words why the line x = 4 is a vertical line. 2. DQ 5-1 Post your response to the following: What similarities and differences do you see between functions and linear equations? Are all linear equations functions?

### Linear Equations and Linear Inequalities

In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities? Give examples. Discuss the important implications arising from this difference.

### Solving for x and y by the method of elimination, and finding the width and length of a rectangle.

2. the perimeter of a rectangle is 26m. the length is 1 m more than twice the width. Find the dimensions What is the length? _____m what is the with?______m 4. Solve by the elimination method x+5y=34 -x+9y=50 5.Solve by the elimination method 5x+5y= -13 -------------(1) 7x-3y= 19 -------------(2) 16. Solv

### Systems of linear equations

Solve the system of equations by graphing ... Solve by the substitution method ... See the attached file.

### Five Questions - Sequences, Linear equations etc.

1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?) 2) Find the counterexample to show that the following statemnet is incorrect. "the sum of any odd numbers is divisible by 4. ( I tried several odd numbers and the answer is always divisible by 4)

### Seven Problems on Determinants, Cramer's Rule and Matrices

Seven practice problems are in the attached file. 1. Use Cramer's rule to solve the system x + y -z = -1 2x - 2y + 3z = -12 X + y - 4z = 13 Solution set is 2. Evaluate the determinate 5 0 0 1 -3 1 1 2 4 3. Use Cramer's rule to solve the system or to determine if it is inconsistent(I) or dependant(

### Manipulating Basic Linear Equations

The following is offered as a solution of the equation -4[x-2(2x-3)]+1= 1/2(4x-6) -4[x-2(2x-3)]+1=8x-12 -4x-4x+6+1=8x-12 -8x+7=8x-12 7= -12 Because 7 = -12 is not a true equation, the equation has no solution. If this is correct, state that there is no solution. If not, explain in detail why it is not correct

### System of Linear Equations

(1.) x-y+2z=13 2x+xy-z=-6 -x+3y + z =-7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this matrix? d. Find the determinant for this matrix. (2) A = [2 -3] [-4 1] [7 4] and B=[ 6 5]

### Matrices, Inverse, Transpose, Determinant, Gaussian Elimination and Cramer's Rule

Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. 1. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires \$12 in computer resources to process and 22 minutes of the accountant'

### The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST.

Attached are problems involving linear equations. Thank you for your help. 1.) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring

### Word Problems Involving Linear Equations in Two Variables

1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floo

### Modeling with Linear Equations

There was several questions ask from my algebra class as a homework which I am having difficulty answering. Please help me solve for them thanks. The equation y = 1.13x + 7.85 represents the average monthly cost in dollars for cable television where x represents the number of years after 1980. Use this equation to answer the

### Solving Systems of Equations

1. y-2x=0 y=8x-9 What is the solution of the system of equations? (i need graph also) 2. r-6s=0 9r-8s=230 What is the solution of the system? 3. x+y= -13 9x+y= -61 What is the solution of the system? 4. (1,2); 6x-5y= -4 2x-7y= -12 is the given ordered pair a solution of the s

### Word Problems and Systems of Equations

Train Tickets At the the Pittsburg zoo, children ride a train for 25 cents, adults pay \$1.00, and Senior citizens 75 cents. On a given day, 1400 passengers paid a total of \$740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders. Manufacturing St

### Algebra : Word Problems and Systems of Equations

Rowing Speed: Hank can row a boat 1 mi upstream (against the current) in 24 min. He can row the same distance downstream in 13min. If both the rowing speed and current speed are constant, find Hank's rowing speed and the speed of the current. Airplane Speed - An airplane flying with the wind from Los Angeles to New York Ci

### Systems of Equations and Inequalities Word Problems

Statistics. After reading an article on the front page of The New York Times titled "You Have to Be Good at Algebra to Figure Out the Best Deal for Long Distance," Rafaella De La Cruz decided to apply her skills in algebra to try to decide between two competing long-distance companies. It was difficult at first to get the compan

### Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.

Complete and please show all the work. Please see attached file for full problem description. 1. List all the factors of 45. 2. Which number is prime? A) 1 B) 12 C) 31 D) 99 3. List all the prime numbers between 25 and 60. 4. Find the GCF for 68, 85, and 153. 5. Find the LCM for 18 and 27. 6. Mul

### Matrix method to solve the linear system of equations

Please see the attached file. 3. A company's employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 22 carbohydrates and 14 grams of prot

### Linear equations and inequalities explained in this solution

Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch). Compute the vol

### Linear Algebra : Orthogonal Basis

Please see the attached file for the fully formatted problems. Problem a. quote a theorem which guarantees that there exists an orthogonal basis for (with standard inner product) made up of eigenvectors of matrix b. Find such a basis . c. Represent the quadratic form by a symmetric matrix. Is Q positive definite?

### Complementary Angles and Systems of Equations

Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five. A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.) B. Graph each of the equations on one rectangular coordinate system. (Hint: Y

### Linear Operators : Finite-dimensional Vector Space, Fields and Mappings

Let V be a finite-dimensional vector space. The base field F may be either R or C here. Let T, an element of the linear mapping of V to V, L(V), be an operator. Suppose that all non-zero elements of V are eigenvectors for T. Show that T is a scalar multiple of the identity map, i.e., that there is a &#955; in the Reals such

### Systems of Equations Word Problems

Supppose a baseball is thrown at 85 miles per hour.The ball will travel 320 ft when hit by a bat swung at 50 miles per hour and will travel 440 ft when hit by a bat swung at 80 miles per hour. Let y be the number of ft traveled by the ball when hit by a bat swung at x miles per hour.(Note: The precceding data is valid for 50 les

### Linear Algebra : Linear Combinations

If you assume {v1, v2, ..., vk} and , and you also assume {v1, v2, ..., vk} are linearly independent and {v1, v2, ..., vk, w} are linearly dependent. How would you show that w can be uniquely expressed as a linear combination of {v1, v2, ..., vk}? Also, if the zero vector is included among the vectors {v1, v2, ..., vk}, w

### Systems of Equations Substitution and Addition Methods

Solve the following system by graphing: 14. x - 2y = -6 y = -3x/2 - 1 15. y < 5x - 2 y > 3x - 2 Solve the following systems by the addition method: 16. x + 2y = 4 3x - 6y = 6 17. 4x - 5y = 20 y = 4/5x - 4 Solve the following systems by the substitution method: 18. 7x - 4y = 26 y =