Practice 4 Solutions

Practice 4 Solutions

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

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