Find a unitary matrix which is not orthogonal and an orthogonal matrix which is not unitary.

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

Maximizing Revenue

The manager of a bicycle shop has found that, at a price (in dollars) of p(x) = 150 - x/4 per bicycle, x bicycles will be sold. a. find an expression for the total revenue from the sale of x bicycles.(revenue = demand x price) b. find the number of bicycle sales that leads to maximum revenue. c. find the maximum revenue ...continues

Linear Programming : Objective Function

Question: A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond- filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of f ...continues

Linear Algebra : Symmetric Polynomials and Inner products

Let be the real vector space of “symmetric” polynomials of degree at most 4, with inner product a. find a basis for V and determine dim V. b. viewing V as a subspace of R) with the same inner product, find the “closest” point in V to the polynomial . Please see the attached file for the fully formatted problems. ...continues

Linear Algebra : Linear transformations, Diagaonalization and Adjoints

Let V be a , but with the weighted inner product, , ,where and . Let be the linear transformation given by T(a,b,c)=(3a-2c,b,3a+10c). a. Show that T can be diagonalized and find a basis for V comprised of eigenvectors of T. b. Find the matrix of the adjoint of T with respect to the basis . Please see the atta ...continues

Linear Algebra : Orthogonal Basis

Please see the attached file for the fully formatted problems. Problem a. quote a theorem which guarantees that there exists an orthogonal basis for (with standard inner product) made up of eigenvectors of matrix b. Find such a basis . c. Represent the quadratic form by a symmetric matrix. Is Q positive definite? ...continues

Matrix Rank and Consistent Systems of Equations

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

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

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

Six lengthy questions on solving linear equations including word problems.

MTH212 Unit 1 – Individual Project A 1. Solve . You must show all work to receive full credit. Show work here: Final Answer: 2. Solve . You must show all work to receive full credit. Show work here Final Answer: 3. The cell phone service for the CEO of a small company is $39.99 a month plus ...continues