Question: (a) For which numbers b (allowing both positive and negative numbers) is the matrix positive definite? (b) Find the factorization A = LDLT when b

(a) For which numbers b (allowing both positive and negative numbers) is the matrix

positive definite?
(b) Find the factorization A = LDLT when b is in the range for positive definiteness.
(c) Find the minimum value (depending on b it might be finite or it might be - ˆž) of the function p(x.y) = x2 + 2bxy + 4y2 - 2y.

LA b. ; )- 4.

Step by Step Solution

★★★★★

3.46 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b 2 b c If b 2 the minimum va... 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 (2128).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Suppose that akj > 0 for k, j N. Set for each k N, and suppose that k=1 Ak converges. a) Prove that b) Show that c) Prove that b) may not hold if akj has both positive and negative values. Consider i...

(a) For which values of c is the matrix positive definite? (b) For the particular value c = 3, carry out elimination to find the factorization A = LDLT. (c) Use your result from part (b) to rewrite...

Prove Theorem 5.24. Let A be an n n symmetric matrix. The quadratic form f (x) x T Ax is a. positive definite if and only if all of the eigenvalues of A are positive. b. positive semidefinite if...

1. [-/4.42 Points]DETAILSBBUNDERSTAT12 7.1.015. MY NOTES ASK YOUR TEACHER Allen's hummingbird ( Selasphorus sasin ) has been studied by zoologist Bill Alther.Suppose a small group of12Allen's...

use this link for questions 1 and 2, https://www.webassign.net/csalt/index.html#/toolset/distributions Oxygen demand is a term biologists use to describe the oxygen needed by tish and other aguatic...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Welcome! Please read this page (in particular) very carefully. Instructions You need to understand how to send your assignments (deliverables) to your instructor. The tabs (bottom of each sheet) in...

9/14/10 12:27 PM Page 321 Chapter dug84356_ch05a.qxd 5 Factoring The sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. Today,...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Which one of the following expenses IS deductible under Section 8-1 of the ITAA (1997)? a). A portion of the running costs of a lawyer's home where that lawyer maintained a home office for...

A biology student uses a simple magnifier to examine the structural features of the wing of an insect. The wing is held 3.50 cm in front of the lens, and the image is formed 25.0 cm from the eye. (a)...

the current ratio of at least 2 . 1 is usually considered to be an acceptable value. true or false

Is it enough to avoid criminal liability to tell an em ployee to take care of the problem? What does this case tell you an officer must do to avoid criminal liability?

Let R4 have the Euclidean inner product. Find two unit vectors that are orthogonal to the three vectors u = (2, 1, -4, 0), v = ( - 1, -1,2, 2), and w = (3, 2, 5,4).

In each part, verify that the Cauchy-Schwarz inequality holds for the given vectors. u = (- 2, 1) and y = (1, 0) using the inner product of Example 2 of Section 6.1

Let W the plane in R3 with equation x - 2y - 3z = 0- Find parametric equations for W

need help on the 3 wrong ones For the just completed year, Hanna Company had net income of $53,000. Balances in the company's current asset and current liability accounts at the beginning and end of...

Chesapeake Yachting Gear is analyzing a proposed project. The company expects to sell 6,000 units, plus or minus 3 percent. The expected variable cost per unit is $11 and the expected fixed costs are...

When the Australian government issues government bonds during a tender, the cumulative aggregate/total demand by bidders is the following: Yield Total cumulative aggregate demand (in AUD million face...