Practice 4 Solutions

# Practice 4 Solutions

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lation f(0) = a, f(n + 1) f(n) = −6 −5 1 0 f(1) = b, n b a = f(n) = − 6 f(n − 1) − 5 f(n − 2) (−5)n 4 5 5 −1 −1 b a + (−1)n 4 −1 −5 1 5 (−1)n (−5)n ( − b − a) + (b + 5a) 4 4 f(n) = [8] Solve the recurrence relation f(0) = a, f(n + 1) f(n) = 16 10 f(1) = b, n f(n) = b a = f(n) = f(n − 1) + 6 f(n − 2) (−2)n 5 2 −6 −1 3 b a + 3n (−2)n ( − b + 3a) + (b + 2a) 5 5 3n 5 36 12 b a b a , 3 × 3 Exercise Set A (distinct roots), November 3 × 3 Exercise Set A (distinct roots) Linear Algebra, Dave Bayer, November , [1] Find An where A is the matrix 200 A = 2 1 1 122 0 0 0 200 000 n n 0 2 3 −3 4 −2 + −1 0 0 + 3 1 1 = 6 2 3 3 −4 2 −5 0 0 622 n λ = 0, 2, 3 An [2] Find An where A is the matrix 122 A = 0 1 0 221 λ = −1, 1, 3 An (−1)n = 2 1 0 −1 121 0 −1 0 3n 00 0 + 0 0 0 0 1 0 + 2 −1 0 1 121 0 −1 0 [3] Find An where A is the matrix 212 A = 0 1 2 012 λ = 0, 2, 3 An 0 0 0 036 1 −1 −2 0n 3n 0 2 −2 + 2n 0 0 1 2 0 0 + = 3 3 0 −1 1 012 0 0 0 [4] Find An where A is the matrix 111 A = 0 1 2 021 λ = −1, 1, 3 An 0 0 0 2 −1 −1 011 1 3n (−1)n 0 1 −1 + 0 0 0 + 0 1 1 = 2 2 2 0 −1 1 0 0 0 011 [5] Find An where A is the matrix 201 A = 2 1 1 201 , 3 × 3 Exercise Set A (distinct roots), November 1 0 −1 00 0 402 n 0 1 3 00 0 + −2 2 −1 + 6 0 3 = 3 2 6 −2 0 2 00 0 402 n λ = 0, 1, 3 An [6] Find An where A is the matrix 121 A = 1 2 2 002 4 −4 2 0 0 −4 125 n n 2 3 0 −2 2 −1 + 0 0 −3 + 1 2 5 = 6 2 3 0 0 0...
View Full Document

## This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

Ask a homework question - tutors are online