(a) Find an orthogonal matrix Q and a diagonal matrix Icirc such that K Q Icirc QT (b) Is K positive definite (c) Solve the second order system d2u t2 A u subject to the initial conditions 103 020 301 du u(0) 0 (0) dt

Question: (a) Find an orthogonal matrix Q and a diagonal matrix Î such that K = Q Î QT. (b) Is K positive definite? (c) Solve

(a) Find an orthogonal matrix Q and a diagonal matrix Î› such that K = Q Î› QT.
(b) Is K positive definite?
(c) Solve the second order system d2u/t2 = A u subject to the initial conditions

103 020 301 du u(0)= | 0 (0) = dt

Step by Step Solution

★★★★★

3.36 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b Yes because K is symmetric and has all positive eigen... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2844).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Answer Exercise 9.5.17 when In Exercise 9.5.17 (a) Find an orthogonal matrix Q and a diagonal matrix Î such that K = Q Î QT. (b) Is K positive definite? (c) Solve the second order system...

Orthogonally diagonalize the matrices in Exercises 1-3 by finding an orthogonal matrix Q and a diagonal matrix D such that QT AQ = D. 1. 2. 3. 1 1 3 0 2

Orthogonally diagonalize the matrices finding an orthogonal matrix Q and a diagonal matrix D such that Q T AQ = D. -2 A -2

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

All questions. 05:50:42 VA; 25% ' ASSIGNMENTNM1.pdf IQ 0+ Numerical Methods-Assignment-l Mathematical Prelimanaries, Taylor's Theorem, Order of Convergence (1) Let L be a real number and let {an} be...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

Werner is the president and CEO of Acme Inc. and this year he took a prospective client to dinner. During the dinner the President and the client discusses a proposed contract for over $6 million and...

a. Show that an A-orthogonal set of nonzero vectors associated with a positive definite matrix is linearly independent. b. Show that if {v(1), v(2), . . . , v(n)} is a set of A-orthogonal nonzero...

Outdoor Weather Inc. makes umbrellas, gazebos, and chaise lounges. The company uses a plantwide overhead allocation approach and assigns overhead to each product using direct labor hours. The company...

The hypothetical information in the following table shows what the situation will be in 2019 if Congress and the president do not use fiscal policy: Year Potential GDP Real GDP Price Level to keep...

Find a formula for a function that has vertical asymptotes x = 1 and x = 3 and horizontal asymptote y = 1.

Find the limits as x → ∞ and as. Use this x → -∞ information, together with intercepts, to give a rough sketch of the graph as in Example 11. 45. y = x(x 2)(1 x) 46. y = (2 +...

(a) Use the Squeeze Theorem to evaluate lim x sin x / x. (b) Graph f(x) = (sin x)/x. How many times does the graph cross the asymptote?

You have invested only in the BlueChip Fund, a mutual fund that invests mainly in stocks. At the moment, the Blue Chip Fund has an expected return of 34% and a volatility of 15%. Your broker suggests...

My appointed company is Restaurant Brands NZ Examine your firm's dividend policy and identify if there have been any major changes over the past five years. (You may want to look at your company's...

1 - In order to establish a sinking fund of $125,000, how much will have to be invested at the end of each year at the rate of 11.2% compounded annually for 8 years? a) O $10,245.73 b) O $11.435.22 C...