assign5 - A n as a linear combination of I 3 , A and A 2 ....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 235 Assignment 5 Due 9:15am, Wednesday Feb 28, 2007. 1. From the Text § 5.3 #31 and #32. § 5.4 #10. § 5.5 #4, #23 and #24. § 5 (Supplementary, page 370+) #1 Justify each answer. 2. According to Example 4 on page 323, the matrix A = 2 4 3 - 4 - 6 - 3 3 3 1 has characteristic polynomial p ( λ ) = - ( λ - 1)( λ + 2) 2 and is not diagonalizable. Find an explicit formula for
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A n as a linear combination of I 3 , A and A 2 . [Hint: First, obtain the remainder polynomial r ( ) when n is divided by p ( ). Dierentiation could be helpful in getting the three coecients of r ( ) explicitly in terms of n . Next, consider the Cayley-Hamilton Theorem.] 1...
View Full Document

Ask a homework question - tutors are online