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Matrices

Real-World Augmented Matrix Problem

From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material. In your own words, please post a

Matrix formulation for interpolation of data

In the attached article, the author proposes a way to interpolate quarterly values when only annual values are available. The only page of this article which is useful for this problem is page 66 (or the second page in this attachment). I am trying to understand the very first step, which is how to get from the statement of t

Properties of Matrices and Vectors

Please show all work for attached problems. 1. Let A, and B be skew- symmetric matrices. Prove that AB is skew symmetric if and only if AB = -BA 2. IF possible find a vector u=(a,b,c) where a, b, c are not all zero so that "u" is orthogonal to both vectors: x= (1,2,1) and y = (1,-1,1) The following are proof questions.

Question on chromatic number of graph, adjacency matrix and list.

Please see attached questions. This is three questions. Question #1 - find the chromatic number of the graph. Question #2 - It might be supposed that if a graph has a large number of vertices and each vertex has a large degree, then the chromatic number would have to be large. Show that this conjecture is incorrect by co

Solve

I have attached the problems. 1. Write the augmented matrix for the given system: Answer HTML Editor 2. Use the system in problem #1. Without interchanging any of the rows in the augmented matrix, what is the first value which will be replaced with zero when using the Gaussian Elimination method? A. -1 B

Vectors, matrices, and bases

Please show all work. Thanks. See attached for proper formatting Question 1 Let B={v1,...,vn} be a basis of a subspace V of Rnx1. Let x be the nonzero vector x=a1v1+...+anvn for scalars ai. Let C={x, v2,...,vn}. a) Show that if a1 is not equal to 0 then C is also a basis. b) Show that if a1 =0 then C is not a basis.

Matrix problem

Four theaters comprise the Cinema Center: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $2 for children, $3.50 for students, and $5.75 for adults. Suppose that on a particular Sunday 240 children, 100 students, and 75 adults attended the evening show in Cinema I; 60 children, 240 students, and

Matrices and word problems

A contractor employs carpenters, electricians, and plumbers, working three shifts per day. The number of labor-hours required for carpenters in shift 1 is 40 hours, electricians in shift 1 is 28 hours, and plumbers in shift 1 is 9 hrs. The number of labor-hours required for carpenters in shift 2 is 18 hours, electricians in shif

Matrices and scalars for inverse covariance

I am unclear as to how some scalars have been calculated. I know what the two vectors and the inverse covariance variance matrix are but please could you clarify the operations required to compute into a single number? There is also a set of data on page two that needs computing along with a general explanation of how to do it.

Linear Equations and Matrices

Gretchen Schmidt plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540. How many share of each stock should she buy? Use the form of " AX=B " equation

Matrices and their Applications

Please help me by showing how these problems on matrices are worked out. (See the Attached Questions File) Answer all questions and show work 1. Find: 2. Find the inverse of: 3. Compute the transpose of A = 4. Introduce slack variables and set up the initial tableau. Do not solve. M

Using Matrices to Solve Problems

See attached for proper formatting of these questions: 1. Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale and sell cookies (C), cakes (K), and muffins

Gaussian Elimination with Scaled Partial Pivoting

Please see attached problem (both Word and pdf version attached). Solve the system 3x1 13x2 | 9x3 | 3x4 = 19 6x1 | 4x2 | x3 18x4 = 34 6x1 - 2x2 + 2x3 + 4x4 - 16 12x1 - 8x2 + 6x3 + 10x4 - 26 by hand using scaled partial pivoting. You may only do the operations on rows that are permitted in Algorithm 6.3 You should nev

Inverses

In your own words can you explain to me how inverses are used to solve linear systems?

Construct the transition matrix.

4. A city is served by three cable TV companies: Xcellent Cable, Your Cable, and Zephyr Cable. A survey of 1000 cable subscribers shows this breakdown of customers from the beginning to the end of August. Company on Company on August 31 August 1 Xcellent Your Zephyr Xcellent 300 50 50

Augmented Matrix and a Real World Problem

From the following augmented matrix (see attachment), first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns.

Scalar matrices with a different from zero.

Problem 1: Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero. Problem 2: Prove that no pair of the following groups of order 8, I8; I4 x I2; I2 x I2; D8; Q, are isomorphic.

Rank and Nonsingular Matrices

Let A be an m x m matrix and B be an n x p matrix. The four fundamental subspaces. Please show each step of your solution. If you have any question or suggestion, please let me know.

Gauss-Jordan Method

Gauss-Jordan method 1. x+y+z=7 x-y+2z=7 2x + 3z+=14 a. 3z+14 z 2 2 z b. -3z - 14z 2 2 z c. -3z +14 z 2 2z d. -3z + 14 2 2z,z 2. 2x -5y +z = 11 3x + y - 6z =1 5x - 4y -5z = 12 a. -29z + 16 15z-31 17 17 z b. 29z +16 15z +31 17 17 z

Create a real world word problem from an augmented matrix.

Please see the attached file for the fully formatted problems. 5. Deliverable Length: 2 - 3 paragraphs Details: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be cr

Matrices and Systems of Equations

1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers represent the number of hats and T-shirt

Provide an example of a matrix that has no solution.

Assistance with Matrices Please see attachment. Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough co

Matrix Rank and Consistent Systems of Equations

We are not using calculator so the steps need to be shown to the solution. 1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent. 2x - y = 7, x + 4y = -5

Systems of Equations and Matrix Methods

1. Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale and sell cookies (C), cakes (K), and muffins (M). They plan to sell their bake goods on Saturday morning