Let (a) Prove that A is diagonalizable if (a d) 2 4bc 0 and is not diagonalizable if (a d) 2 4bc 0 (b) Find two examples to demonstrate that if (a b) 2 4bc 0, then A may or may not be diagonalizable b A d...

Recall Exercise 35 in Section 41 We repeat the relevant parts of its solution here a If the eigenval ...

Let (a) Prove that A is diagonalizable if (a -d) 2 + 4bc > 0 and is

Question:

Let

(a) Prove that A is diagonalizable if (a -d)² + 4bc > 0 and is not diagonalizable if (a - d)² + 4bc < 0.
(b) Find two examples to demonstrate that if (a - b)² + 4bc = 0, then A may or may not be diagonalizable.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 13, 2018 07:06 AM

See More Questions

In Exercises 1-3, let T: V W be a linear transformation between finite-dimensional vector spaces V and W Let B and C be bases for V and W, respectively, and let A = [T] CB. 1. Show that nullity(T) =...
Let A be a diagonalizable n x n matrix. Prove that if B is any matrix that is similar to A. then B is diagonalizable.
Let H be a nonempty, closed, bounded subset of Rn. a) Suppose that f : H Rm is continuous. Prove that is finite and there exists an x0 H such that ||f(x0)|| = ||f||H. b) A sequence of functions fk: H...
Khairul has been working with Tun Hamid Energy Bhd since 1 February 2009 as a Human Resource Executive. Beginning 1 January 2014, he was promoted as Human Resource Manager. Details of his...
A Porsche sports car can accelerate at 14 m / s2. (a) Is this acceleration greater than, less than, or equal to 14 ft / s2? Explain. (b) Determine the acceleration of a Porsche in ft / s2.
Castaway Boats, a merchant boat dealer, sold a boat to Gilligan, a consumer buyer for cash. The sale took place at the Island Marina, Castaway Boats's place of business. Gilligan, was about to go on...
What is an input/output control system designed to do? How is input controlled? How is output controlled? LO.1
In what types of situations is conducting a census more appropriate than sampling? When is sampling more appropriate than taking a census?
Baka Corporation applies manufacturing overhead on the basis of direct labor-hours. At the beginning of the most recent year, the company based its predetermined overhead rate on total estimated...
Coffee Blending and Sales Hill-O-Beans Coffee Company blends four component beans into three final blends of coffee: one is sold to luxury hotels, another to restaurants, and the third to...
What significant regulatory trends are affecting accounting in general today? How do these regulatory trends affect the field of managerial accounting?
Explain the importance of having guidelines for ethical behaviour.
What is the length of the nail reported to the correct number of significant figures? 2 3 4 5 6 7 Centimeters
Figure < 4 ft/s 45 0.75 ft 3 ft/s 1.50 ft 1 of 1 < Part A Determine the velocity of point A on the rim of the gear at the instant shown.(Figure 1) Enter the x and y components of the velocity...
what ways can leaders facilitate cognitive reframing and emotional regulation techniques to promote constructive conflict resolution ?
What is the level of sales needed to achieve a 10% return on an investment of $10,000,000 for a restaurant (the restaurant has main products it sells: food, beverage and gift shop items) and cover...
1. An online computer assembling mobile phone Application provides interfaces for end users to assemble computers by selecting computer accessories with different configurations from different...
1. (# 3.21, Text) Plot the longitudinal and transverse coefficients of thermal expansion for a unidirectional glass-polyester composite as functions of fiber volume fraction. Assume the following...
The function f is such that f(x) = 3x 2 for x 0. The function g is such that g(x) = 2x 2 8 for x k, where k is a constant. a. Find the greatest value of k for which the composite function fg can...
Write a declaration for each of the following: a. A line that extends from point (60, 100) to point (30, 90) b. A rectangle that is 20 pixels wide, 100 pixels high, and has its upper-left corner at...
Suppose a new threshold of change, Î mg/dL, is proposed for establishing compliance. We wish to use a level of Î such that the compliance measures in Problems 5.36 and 5.38 for the...
Suppose we consider the serum vitamin E assay as a screening test for compliance with vitamin E supplementation. Participants whose change in serum vitamin E is ¥ Î mg/dL will be considered...
Plot the distribution of z-scores for smokers and nonsmokers separately. Do these distributions look normal? Do smoking and pulmonary function seem in any way related in these data?
Suppose Universal Forests current stock price is $59.00 and it is likely to pay a $0.57 dividend next year. Since analysts estimate Universal Forest will have a 13.8 percent growth rate, what is its...
ABC Company engaged in the following transaction in October 2 0 1 7 Oct 7 Sold Merchandise on credit to L Barrett $ 6 0 0 0 8 Purchased merchandise on credit from Bennett Company $ 1 2 , 0 0 0 . 9...
1. Use the Excel file Asset Allocation Data to determine the following: a.Variances for the individual assets b. Standard deviations for the individual assets c.Covariances between each pair of...

Let (a) Prove that A is diagonalizable if (a -d) 2 + 4bc > 0 and is

Question:

b. A d

Step by Step Answer:

Recall Exercise 35 in Section 41 We repeat the relevant parts of its solution here a If the eigenval...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions