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Matrices

Systems of Equations : Real World Situations and Determinants

1. In real-world situations, what is the advantage of using the Method of Substitution to solve a system of equations rather than using the Method of Addition? 2. When solving a 3x3 determinant, we broke the determinant down into a sequence of 2x2 determinants, remembering to alternate the signs of the leading coefficients in

Equations, point of intesection, plane of intersection

14) Solve the following system of equations x1 - 3 x2 =5 -x1 + x2 + 5 x3= 2 x2 + x3 =0 15) Determine if the system is consistent. Do not completely solve x1 + 3 x3 =2 x2-3x4 =3 -2x2+ 3x3 + 2 x4= 1 7 x4= -5 17) Do the three lines x1 -4 x2 = 1, 2 x1 -x2 = -3, - x1 -3 x2 =4 , have a common point of intersection? Exp

Matrices

Need to see problems on attachment done to further grasp concepts I am missing. Please do not leave out any details in solving the problems. If I ask questions please answer them in detail and please make everything simple and clear to understand. My goal is to apply what you solve to other problems I want to work on on my ow

Matricies

Need to see problems on attachment done to further grasp concepts I am missing. Please do not leave out any details in solving the problems. If I ask questions please answer them in detail and please make everything simple and clear to understand. My goal is to apply what you solve to other problems I want to work on on my ow

Matrices : Gauss-Jordan Elimination

65. A father, when dying, gave to his sons 30 barrels, of which 10 were full of wine, 10 were half full, and the last 10 were empty. Divide the wine and flasks so that there will be equal division among the three sons of both wine and barrels. Find all the solutions of the problem. (from Alcuin) 4, 5 Find all solutions of the

Matrices: Gaussian Elimination, Calculation Time and Cramer's Rule

Questions: a) How many multiplications are necessary to find the determinants of matrices which are 2x2, 3x3, 4x4? b) The number of multiplications for an nxn matrix may be found in terms of the number for an (n-1)x(n-1) matrix. FIND THIS FORMULA and use it to obtain the number of multiplications for a 10x10 matrix. c) Fo

System of Equations: Matrix Form and Eigenvalues

Consider the attached system of equations. (a) Write the system in the given matrix form {see attachment} (b) Determine the eigenvalues of A in terms of the parameter {see attachment} (c) The qualitative nature of solutions depends on .... (d) Sketch a typical phase portrait... Please see attachment for complete set of

Finding Adjoint Operators

Problem: Find the adjoint operator and its domain for: a) . (Assume is continuously differentiable and is continuous on the interval . This is the answer, I just need to see the steps to arrive there: , with boundary conditions . b) Again, here is the answer, but I need to see the solution method:

Matrix Proof

Prove that ||x^(k) - x|| <= (||T||^k)(||x^(0) - x||) and ||x^(k) - x|| <= (||T||^k/(1-||T||))(||x^(1)-x^(0)||), where T is an n x n matrix with ||T|| < 1 and x^(k)=Tx^(k-1)+c, k=1,2,..., with x^(0) arbitrary, c belonging to R^n, and x=Tx+c.

Matrix Norm

The frobenius norm (which I know is not a natural norm)is defined for an n x n matrix A by ||A||_f = (sum i=1 to n, sum j=1 to n, |a_ij|^2)^1/2 Please show that ||.||_f is a matrix norm. That is, satisfy the five axioms. NOte: _ is subscript.

Least Square Problems

Let P = A(A^TA)^-1A^T, where A is an mxn matrix of rank n. (1) Show that P^2 = P. (2) Prove P^k = P for K = 1,2,.... (3) Show that P is symmetric. ____________________________________________________ Let A&#1028;R^(mxn) and let r be a solution to the least square problem Ax=b. Show that a vector y&#1028;R^n

Isomorphism Example Problem

If G ={a + b*sqrt2 | a,b rational} and H = {matrix a 2b, b a | a,b rational}, H is a 2 x 2 matrix - a 2b b a show that G and H are isomorphic under addition. Prove that G and H are closed under multiplication. I know I need to define the function map first, but I don't know what it is in this problem, let alone prove

Angles and matrices

Project 3 2. Lance Armstrong won the 2003 Tour de France. The wheel on his bike had a 63 inch diameter. His average speed was 40 km / hour. What was the angular speed of the wheel in revolutions per hour? 3. A construction company is making picnic pavilions where the roof will be supported by two sets of beams. The bea

Matrices : Vector Equations

Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution. 1) Compute u + v and u - 2v u = -1 ; v = -3 2 -1 2) Display the following vector

Decision making using matrix reduction

I am having problems coming up with the equations(systems)to use for the following word problem. I don't usually have a problem with solving matrices infact I like them but I can't even get started on this problem. A company produces two products, A and B For each unit of A sold the profit is $8, and for each unit of B the pr

Matrix Reduction

I am to use matrix reduction on this problem. I can solve systems by matrixs with out any problem but I can't seem to set up the two equations for this problem so that I can even turn them into a matrix and solve. A company produces desks on both the east and west coast. The east coast plant, fixed costs are 16000 per year an

Multiply matrices

Multiply matrix a by matrix b matrix a: row 1 = [0 1 2] row 2 = [-1 4 .5] row 3 = [1 3 0] matrix b: row 1 = [3 -1 5] row 2 = [0 2 2] row 3 = [4 -6 0]

Matrix Series : Trace Log and Log Det

Please see the attached file for the fully formatted problems. Let K be an nxn matrix and  a small number. Imitating ..... valid for small x, it is natural to define .... Explain why this makes sense. Prove trace log = log det(I + K) Still with  small so that everything makes sense. Hint: What is I &#8722; K +2K2

Diagonal Matrix

Diagoalize te given matrix: A= 3 1 1 1 0 2 1 2 0 an find an orthogonal matrix P such that P'-1(Pinverse)AP is diagonal.

Symmetric matrix

What is the symmetric matrix of the quadratic form 2x^2 - 8xy + 4y^2?

Matrices and equations

Protein, carbohydrates, and fats can be obtained from three foods. Each ounce of food I contains 5 grams of protein, 10 grams of carbohydrates, and 40 grams of fat. Each ounce of Food II contains 10 grams of protein, 5 grams of carbohydrates, and 30 grams of fat. Each ounce of Food III contains 15 grams of protein, 15 grams o