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Linear Algebra

Linear Programming

Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x

Graphing linear inequalities

Solve the following system of linear inequalities by graphing. 3x+4y is less than or equal to 12 x+3y is less than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0

Linear Programming, Equations of Lines and Word Problems

1) f(x)=3x(2x-1). f(-1)= A)7 (B)11 (C)-6 (D) 9 2) The slope of the line through the points (3,4)and (-1,7) is A)4/3 (B) ¾ (C) -3/4 (D) 7/4 3)The line 6x + 9y=8 has slope A) -2/3 (B)-6 (C) 4/3 (D) 9 4)Select the line parallel to 6x +14y =20 A) 3x-7y=15(B) 7x-3y=8 (C) y=20/6x+14 (D)y= -3/7x+11/7 5) A revenue f

Linear Equations and Systems of Equations with Parameters

Please help with the following problems. Provide step by step calculations. Find the slope of each line that has a slope x=5y Find an equation in the form y=ms +b (where possible) for each line. Through (3,-5) parallel to y= 4 Graph each linear equation defined as follows; 3x - 5y =15 Solve each system of equat

Matrices

Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them. Copy the questions to a Microsoft Word document and use an equation editor to enter the answers. Please answer the following questions

Algebra Questions

See attached file for full problem description. 24. Complete the ordered pairs so that each is a solution for the given equation. 3x + 4y = 12 46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula F = 9/5C + 32 . What is the Fahrenheit temperature that corresponds

Logic : Decidable Systems

Question Let (N, <) be the model with universe N and the "less than" relation. Show that Th(N, <) is decidable. Solution Reduce Th(AJ, <) to Th(fV, +), which we've already shown to be decidable. To do so, show how to convert a sentence 0, over the language of Th(A(, <), to a sentence 02 over the language of Th(AF, +) w

Systems of Linear Equations

1. Solve the following systems of linear equations. Solve one using addition and one using substitution. State which method you are using for which system... a) 4x - 3y = 10 & y - 20 = -6x b) y = 3x + 6 & -6x + 2y = 12 2. You are buying coffee beans for your new business, "The Algebra Café." You

Evaluating Functions and Systems of Linear Equations and Inequalities

(See attached file for full problem description) 1. Graph f(x) = -2x + 2. 2. Rewrite the equation -x - 10y = 50 as a function of x. 3. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 4. Given f(x) = 4x - 5, find f(a - 1). A) 4a - 9 B) 4a - 6 C) a - 2 D) a - 9 5. Graph the inequality.

Linear Equations and Inequalities

1) Given one point on the graph (-3, -5) and the slope, m = -2, develop an equation in the slope-intercept format Lecture). 2) Given one point on the graph (- 2/3, 2/5) and the slope, m = - 3, develop an equation in the slope-intercept format(Lecture). 3) Given the following two points, (- 4, - 2) & (-1, - 5),develop an

Linear Equations

1. You are given the following system of linear equations: 3x - 2y + z = 2 -x + y = 3 -2y + 6 = -1 Provide a coefficient matrix corresponding to the system of linear equations. What is the inverse of this matrix? What is the transpose of this matrix? Find the determinant for this matrix. Calculate the following

Solving the linear system using Gaussian elimination

Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. Show specifically how row operations can be used to solve the matrix. State the solution. Substitute the solution back into the equation to verify the solution. O

General vector spaces - rank and nullity

10. Let A = a11 a12 a13 Show that A has rank 2 if and only if one or more of a21 a22 a23 the determinants a11 a12 a11 a13 a12 a13 a21 a22 a21 a23 a22 a23 are non zero. 14. Use the result in Exercise 10 to show that the set of points (x, y, z) in R3 for which the matrix

Dependency Equation and Feasibility Analysis

4. The Volta Battery Company manufactures AA, A. C, and D batteries in each of four plants. The daily production (in 1000's) for the four plants is given the following table: [TABLE] (a) The vectors that represent the production at the various plants are not linearly independent. Show this and find a dependency equation. (b)

Algebra

Please see the attached file for complete description 1. Solve the system by graphing. x + y = 4 -x + y = 2 2. Determine which two equations represent perpendicular lines. 3. Solve the system by graphing. 3x + y = 6 3x - y = 0 4. Graph the inequality y < -3 5. Solve the following system of linear inequalit

General vector spaces - basis and dimension

10. Find the coordinate vector of p relative to the basis S = {p1, p2, p3}. (a) p = 4 - 3x + x2; p1 = 1, p2 = x, p3 = x2 (b) p = 2 - x + x2; p1 = 1 + x, p2 = 1 + x2, p3 = x + x2 22. Find the standard basis vectors that can be added to the set {v1, v2} to produce a basis for R4. v1 = (1, -4, 2, -3), v2 = (-3, 8, -4,

General Vector Spaces - Linear Independence

2. Which of the following sets of vectors in R3 are linearly dependent? a) (4, -1, 2), (-4, 10, 2) b) (-3, 0, 4), (5, -1, 2), (1, 1, 3) c) (8, -1, 3), (4, 0, 1) d) (-2, 0, 1), (3, 2, 5), (6, -1, 1), (7, 0, -2) 4. Which of the following sets of vectors in P2 are linearly dependent? a) 2 - x + 4x2, 3 + 6x + 2x2, 2

Systems of Linear Equations Word Problems

1. Leon drove 270 to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10mph faster than Leon, how fast did each of them drive? 2. A company specializing in magazine sales over the telephone found that in 2500 phone calls, 360 resulted in sales and were made by a male caller, and 480 resulted in sal

Linear Equations:Predicted sales of a company

Suppose the sales of a company are given by S(x) = $200x + $20,000 where x is measured in years and x = 0 corresponds to the year 1996. Find the predicted sales in the year 2002 assuming the trend continues.

Graphing and Solving Systems of Linear Equations

See attached file for full problem description. Graph y = -1. Solve the system by addition or substitution. 3x + 6y = 0 x = Find the slope of the line passing through the points (-4, 10) and (-6, 5). Solve: 6x + 4(3x - 2) = 6x + 2 Graph 3x + y = 3. Let y vary directly with x, with

Linear Equation

(1) Given a line containing the points (1, 4), (2, 7), and (3, 10) determine the slope-intercept form of the equation and provide one additional point on this line, and graph the function.