Explore BrainMass

Explore BrainMass

    Linear Algebra

    BrainMass Solutions Available for Instant Download

    Matrices

    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. One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services. It costs $5 in materials and req

    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

    The Solution of a System of Equations

    1. How do you interpret the solution of a system of equations by the corresponding graph? Please provide example. 2. What is the situation when two linear inequalities have no solution? 3. What are the conditions when the solution of a system of linear inequalities will be in the first quadrant?

    Explain 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 question

    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

    Matlab: Linear Least-Squares Fit

    Please provide a Matlab Script for Linear Square fit. Write Linear Square fit mat lab script Input X1, X2 ............................Xn Y1, Y2..............................Yn Representing order pairs (X1, Y1) (X2, Y2) ........ (Xn, Yn) Output should a0 and a1 from page 484 I attached few description pa

    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

    Linear Equations Word Problems

    In Atlantic City, Nick played the slot machines for 12 h. He lost $45 an hour. Use real numbers to represent the change in Nick's financial status at the end of 12 h. Compose a note explaining how you arrived at the solution. What difficulties (if any) did you encounter?

    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)

    Euclidean Spaces and Subspaces..

    2. Consider the set S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)}. (a) What value(s) of t will make the set linearly independent? (1)) Choosinig a value of t that will make S linearly dependent fnd the Euclidean (linear) equation form of the subspace spanned by S.

    Using Matrix to Solve Linear System of Equations

    See attached file for full problem description. 1. Find the equation of the line shown: (see attachment). 2. 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. Write the augmented matrix of the system: (see attach

    Linear approximation problem

    A = alpha , B = beta Show that the linear approximation of the function f(x,y) = x^a y^B at (1,1) is x^a Y^B = 1 + a(x-1) + B(y-1) .

    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

    Solving Systems of Linear Equations

    Determine whether this system has a unique solution, no solution, or infinitely many solutions. If a solution exists, write it down. y = x x + z = 4