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Matrices

Matrices

I need more understanding and examples to form my own opinion for discussion the how to set up and solve with the below parameters For this Discussion Board, 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,

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

Constructing a Matrix with the Given Characteristics

Linear Algebra a. Construct a 3 x 3 matrix A with C(A) belonging to N(A). b. Construct a 3 x 3 matrix A with N(A) belonging to C(A). c. Do you think there can be a 3 x 3 matrix A with N(A) = C(A)? d. Construct a 4 x 4 matrix A with C(A) = N(A).

Orthogonal Matrices' Transposes

Please see the attachment for the properly-formatted question on transposing an orthogonal matrix. Please solve for part (b). Please explain each step of your solution. Thank you.

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

Augmented Matrix to Solve a System of Equations

The augmented matrix of a linear system has been reduced by row operations to the form shown. explain step by step no matter how small the detail In each case, continue the appropriate operations and describe the solution set of the original system. a + b - c = 7, a - b + c = 5, 3a + b - c = -1.

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

Matrices and Solutions

Matrices are the most common and effective way to solve systems of linear equations. However, not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution. Provide an example of a matrix that has no solution. Use

Find a Unitary Matrix Which is Not Orthogonal

This is for #1 section 8.4 in Hoffman and Kunze's Linear Algebra book. Any help and detailed explanations will be greatly appreciated! Find a unitary matrix which is not orthogonal and an orthogonal matrix which is not unitary.

Invertible Matrices and Orthonormal Basis

1. (10 pts) Prove or disprove: Let {v1, . . . , vn} be a basis for Rn. If A is an invertible n × n matrix, then {Av1, . . ., Avn} is also a basis for Rn. 2. (20 pts) In P3, define the function ..... (a) Show that p, q is an inner product. (b) Find an orthonormal basis for P3. (c) Express 7x2 − 2 as a linear comb

Linearly Independent Vectors and Invertible Matrices

If you let {v1, v2,...,vk} be linearly independent vectors in and A & B are n x n matrices. If you assume A is invertible how would you show that {A(v1), A(v2,)...,A(vk)} are linearly independent? Also, if you know that {v1, v2,...,vk} are linearly independent and {B(v1), B(v2,)...,B(vk)} are linearly independent, how do yo

Matrices and Systems of Equations

A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equatio

Matrix Determinants

Show that the determinant for the following matrix equals zero for any value of k other than k=0. Please see the attached file for the fully formatted problem.

Square Matrix with Determinant Equal to 0 and Basis for a Solution Space

1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax=b then every solution to this equation must have the form x=X+xot where xo is a solution of Ax=0. 2) Find a basis for the solution space of the following system of equations. x- 2x2+ x3 =-4 -2x +3x2 + x4=6 3x -