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Linear Algebra

Systems of Linear Equations : Row Operations and Solutions

1. Find the augmented matrix for each system of linear equations: a. 5x1 + 7x2 + 8x3 = 3 -2x1 + 4x2 + 9x3 = 3 3x1 - 6x2 + x3 = 1 b. 4x1 + x2 - 7x3 = 6 5x1 + 7x2 + 2x3 = 3 5x1 + 2x2 + 5x3 = 7 c. 3x1 - 2x2 + 2x3 = 7 5x1 + 7x2 + 3x3 = 3 -5x1 + 6x2 - 8x3 = -5 2. Using elementary row operations reduce each of the augm

Linear functional on N U 0

Let H = l^2(N U 0) (a) Show that if {a_n} is in H, then the power series sum_{n=0}^infty a_n z^n has radius of convergence >= 1. (b) If |b| < 1 and linear functional L: H-->F (F is either the real or the complex field) is defined by L({a_n}) = sum_{n=0}^infty a_n b^n, find the vector h_0 in H such that L(h) = < h, h_0 >

Working With Matrices

Question: Any matrix B which is formed by the eigen vectors of a matrix A reduces the given matrix A to the diagonal form by the transformation (inverse of B)AB. i.e., (inverse of B)AB = diagonal matrix Please view the attachment to see the fully formatted problem.

Find the eigen values and eigen vectors of the matrix

Find the eigen values and eigen vectors of the matrix A = [9, -1 , 9; 3 , -1 , 3; -7 , 1 , -7] Also find the corresponding eigen spaces for the matrix A. Find a matrix B which reduce the given matrix A to the diagonal form by the transformation B^(-1)AB.

Estimate the linear trend equation for the production series

Estimate line and find linear trend equation of the attached. A. Estimate the linear trend equation for the production series by drawing a line through the data. B. What is the average annual decrease in production? C. Based in the trend equation, what is the forecast for the year 2005? (See attached file for full pr

Computer Applications & Substitution, Elimination and Matrices

What computer applications can be used to graph systems of equations? Have you ever personally used any applications to graph an equation? In what circumstances does it make more sense to graph a system than to use the substitution, elimination, or matrix methods?

Characteristic equation of a matrix and inverse of a matrix

Linear Algebra Matrices Eigen Values and Eigen Vectors(I) Find the characteristic equation of the matrix A = [1, 3, 7; 4, 2, 3; 1, 2, 1] Show that the equation is satisfied by and hence obtain the inverse of the given matrix. The fully formatted problem is in the attached f

Systems of Equations and Linear Programming: Six Word Problems

See the attached file. 1. A small school held a fund raiser. A total of 23 adults and children attended. Each adult paid $10, and each child paid $2 to attend. If a total of $86 was raised, use a system of equations to determine how many adults and how many children attended. Solve the system using Gaussian Elimination. 2.

Solutions of the system of equations

Determine the solutions of the system of equations whose matrix is row equivalent to 1 0 &#8722;1 |1 0 1 3 |1 0 0 0 |0 Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.

System of Equations Application Word Problem : Quarters and Dimes

Can I please find out what I am doing incorrectly with the following problem? "I have seventy five coins in my pocket made up of quarters and dimes. If the total value of the coins is $12.45, how many of each coin do I have?" q + d = 75 Let q represent quarters (0.25)q + (0.10)d = 12

Word Problems as Systems of Equations and Solving the Systems

Write a system of equations and then solve the following using matrix inverses. Consider a company that specializes in gourmet chocolate baked goods-chocolate muffins, cookies and brownies. Each chocolate muffin requires 2 units of chocolate, 3 units of flour and 2 units of sugar. Each chocolate cookie requires 1 unit of c

Equation of an Ellipse, Interest and Lotto Probability

Several state and federal government spokespersons who use linear equations in a variety of ways. 1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse

Slope and Intercept Calculations - Women, Pay and Education

Real Life Application of Linear Equations: A mathematician has developed a model indicating a woman with x years of education can expect to earn y = 1200x + 6300 dollars a year. What is the y-intercept for this model? Describe what it means in terms of the model. What is the slope for the model? Describe what this means in

Matrix Representation of a Linear Operator on Vector Space

1) Let A be a linear operator on n-dimensional vector space V if {see attachment}. For some {see attachment}, prove that matrix representation {see attachment} of A with respect to a basis ... Please see attachment for complete question.