Question: (a) Show that one of the nondiagonal elements, but not both, must be negative in order for the eigen values to be nonreal. (b) Show

(a) Show that one of the nondiagonal elements, but not both, must be negative in order for the eigen values to be nonreal.
(b) Show that eigenvalues are imaginary (Î± = 0) if and only if Tr A = 0 and |A| > 0.

Step by Step Solution

★★★★★

3.30 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The characteristic equation is with solution Hence for bc ... 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)

947-M-L-A-L-S (4999).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

In Exercise 5.62, we see that students who study by giving themselves quizzes recall a greater proportion of words than students who study by reading. In Exercise 5.62 we see that there is an effect,...

Show that if has length one. What if V0 then v/lvl

Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

What is Exercise 32-45? I don't quite understand it, so I'm not sure if my work or answers are correct. Linear Algebra Lab Exercises Linear algebra deals with vectors and linear functions that act on...

1) Find all real solutions of: 4 2 2 x + x =3 2 x 4 + x23=0 4 2 2 2 x 2 x +3 x 3=0 x ( 21)=0 2 x 2 ( x 21)+ 3 ( 2 x2 +3 ) ( x 21 ) =0 ( 2 x2 +3 ) =0 2 2 x =3 3 x 2= 2 3 x= 2 3 x= i 2 2) Given the...

Please answer the question below. You need to read the imaginary case Tesla-motorcycles in order to answer the questions. -What are the primary components of Tesla Motorcycles value chain? The answer...

Using the pages below, answer the following questions; Chapter 10 Read P.218- 223 Answer 223 Q.1-3 Read P.224-234 Answer P.234 Q.1-3 AS YOU READ . -. . YOU WILL LEARN ' To dene entertainment...

Please solve this Model question on excel and provide the formula on how to do it: You are thinking of opening a Broadway play, I Love You, Youre Mediocre, Now Get Better! It will cost $7 million to...

#4 Part A - Magnetic Field Lines and Kick Strengths . In this part of the experiment we will map the magnetic field around a permanent bar magnet and measure the strength of the magnetic field (B) at...

A camera is being used with the correct exposure at f/4 and a shutter speed of 1/32 s. In order to stop a fast-moving subject, the shutter speed is changed to 1/256 s. Find the new f -stop that...

Lusk Corporation produces and sells 14,800 units of Product X each month. The selling price of Product X is $30 per unit, and variable expenses are $24 per unit. A study has been made concerning...

A private company has a bank loan with a banking covenant related to profitability. Which of the following statements about the acquisition and payment cycle is likely true? The private company may...

List the major federal statutes dealing with the regulation of equal rights in employment.

In Problems 1 through 10, apply Theorem 1 to determine the type of the critical point (0 , 0) and whether it is asymptotically stable, stable, or unstable. Verify your conclusion by using a computer...

In Problems 1 through 4, show that the given system is almost linear with (0 , 0) as a critical point, and classify this critical point as to type and stability. Use a computer system or graphing...

In Problems 1 through 8, find the critical point or points of the given autonomous system, and thereby match each system with its phase portrait among Figs. 9.1.12 through 9.1.19. dx dt = 2x - y, dy...

12. Which is the correct sequence of accounting procedures? (5 Points) O a. Journal, ledger, trial balance, financial statements O b. Ledger, trial balance, journal, financial statements O c....

Words were displayed on a computer screen with background colors of red and blue, Results from scores on a test of word recall are given below. Use a 0.05 significance level to test the claim that...

(Book exercise 1.2.8) Determine how many terms in the Taylor series for e x are needed to compute e with 13 correct decimal digits, round