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# Matrices

### Matrix theory and analysis homework

Please see the attached document regarding homework specifics. Thank-you so much for your help. For each eigenvalue find the corresponding eigenspace and a set of vectors which span the eigenspace.

### Matrix inverse solution

Please see attached file Solve all these problems using matrix inverses. You have seen these problems before and have used other means to solve them, please disregard those solutions and solve these using only matrix inverses.

### 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.

### Inverse Matrices used to solve linear systems

Problem1.How are the inverse Matrices used to solve linear systems. Explain in your own words with example. Problem 2. In the matrix Algebra why does there have to be right and left distributive properties.

### Matlab and numerical analysis

The problems I need solved are attached. Please provide as much detail as possible and include comments for the code done in MATLAB, so I can understand. Thanks Assume that a computer can perform 10^6 multiplications per second. Estimate the time that it would take to evaluate the determinant of a 100x100 matrix...

### Matrix equation - Need help in solving AX=b equations

Need help in solving AX=b equations; [ 200 ] [ 4 ] -120 10 A= -241 ,B= 11 , AX=B a) [0,8,9] b) [2,6,-9] c) [3, 7, 8] d) [3,6,-10]

### 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

### Matrix with more than one solution

I need an example of a matrix that has more than one solution.

### Matrix with no solution

I need an example of a matrix that has no solution. I also need to know how to use row operations to show why the problem has no solution.

### Practice Questions - Matrices and Equations

Can you explain to me how these problems are solved? (Please see the attached questions file).

### 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

### 3)Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be expressed as matrices. Help them solve the following problems. 4. The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g of fat, and 17g of carbohydrates. One cup of whole milk contains 150 calories, 8g of protein, 8g of fat, and 11g of carbohydrates. Write 1 x 4 matrices P, G, and M that represent the nutritional values of each food. Find 3P+2G+2M and tell what the entries represent.

3)Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can

### Working with Rotational Matrices

R is a 3x3 matrix. What property is required of R for it to be an orthogonal matrix. and (I:-) a rotation matrix? Write down the matrix that effects a rotation by angle theta about the y-axis. See attachment for the rest of the questions.

### 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

### Matrix problems

See attached matrices

From Determinants. (From Determinants. Prove the proposition without using Cofactors/Cramer's rule.) See Attached

### Linear Algebra - Cofactors and Cramer's Rule

Please see the attached file. Please kindly show each step of your solution. Thank you. Show that if the entries of a matrix A are integers, then det A is an integer. (Hint: use induction)

### Solve the system using Gaussian elimination.

Please see the attached file. Solve the system using Gaussian elimination. 2x + y = 1 -2x + 3y = -13 Find the indicated matrix. Let A = [■(1&3@2&4)] and B = [■(0&4@-1&6)] Find 2A + B. For the given matrix A, find -A. A = [■(3&-7@ -6&7)]

### Inverses

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

### Transpose this augmented matrix

7 questions in the attached file.

### 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

### Hilbert Matrices

Please see the attached file. Solve the system of equations. Use Gaussian elimination. Find the Doolittle LU decomposition of H5 with scaled partial pivoting.

### Gaussian Elimination and Gauss-Siedel

Please see attached pdf file with 4 problems on Gauss Elimination as well as Gauss-Siedel.

### Optimal Assignment Problem for an Array

How do you solve the optimal assignment problem for the following array by solving two dual problems? Also, how many optimal solutions are there for the array and why? J1 | J2 | J3 | J4 | J5 P1| 2 | 3 | 4 | 3 | 5 P2| 1 | 3 | 2 | 1 | 3 P3| 3 | 5 | 2 | 3 | 3 P4| 4 | 4 | 2 | 1 | 4 P5| 3 | 1 | 4 | 4 |

### 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.

### Orthogonal basis to find matrix

I think matrix A is created by the given vectors (1,0,1) and (0,1,-2) in this case. The material is from Orthogonal Bases. Please explain each step of your solution. Construct the matrix proj(v)....

### Check from the formula for the projection matrix

The material attached is from Inconsistent Systems and Projection. Please show each step of your solution. If you have any question or suggestion on my posting, please let me know.

### Showing a matrix is totally unimodular.

This problem was a sample exam question taken from a text book. This problem is about showing a matrix is TU. This problem can be found in the Wolsey text book called "Integer Programming". A useful resource is "Integer and Combinatorial optimization" by Wolsey and Nemhauser.

### I need a matrix that has no solution

I need a matrix with no solution, use row operations to matrix that has no solution. Use row operations to show why it has no unique solution. Also some matrices that have more then one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough constraints