a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn

Chapter 7, Problem 8

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn. (Hint: Bn = O.) b. Let J be an n n Jordan block with eigenvalue . Show that etJ = et tet 1 2 t 2et 1 (n1)! tn1et et tet 1 (n2)! tn2et . . . . . . ... et tet et . (Hint: Write J = I + B, and use Exercise 2.1.15 to find J k.)

Questions & Answers

QUESTION:

a. Consider the n n matrix B = 0 1 0 1 . . . . . . 0 1 0 . Calculate B2, B3, . . . , Bn. (Hint: Bn = O.) b. Let J be an n n Jordan block with eigenvalue . Show that etJ = et tet 1 2 t 2et 1 (n1)! tn1et et tet 1 (n2)! tn2et . . . . . . ... et tet et . (Hint: Write J = I + B, and use Exercise 2.1.15 to find J k.)

ANSWER:

Step 1 of 4

Given  matrix is

                   

To calculate .

Here,  is the matrix with 1 as an element in the first upper diagonal.

On multiplying using the rule of matrix multiplication,

                         

So,  is the matrix with 1 as an element in the second upper diagonal.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back