Solution Found!
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)
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.