Practice 4 Solutions

201 1 1 0 111 1 0 1 1 1 a 0 2 1 1 111 0 00 111

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Unformatted text preview: 2, 4 An 1 −1 −1 110 1 −1 2 n n 1 2 4 1 1 + 1 1 0 + −1 1 −2 = −1 3 2 6 −1 1 1 000 2 −2 4 3 × 3 Exercise Set K (symmetric matrices), November , 3 × 3 Exercise Set K (symmetric matrices) Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix −3 1 0 A = 1 −2 −1 0 −1 −3 1 −1 −1 101 1 2 −1 −3t −t e e −1 0 0 0 + e 2 1 1 + 4 −2 = 3 2 6 −1 1 1 101 −1 −2 1 −4t λ = −4, −3, −1 eAt [2] Find eAt where A is the matrix −1 −1 −1 0 A = −1 −2 −1 0 −2 111 0 0 0 4 −2 −2 −2t 1 e 1 1 1 + e 0 1 −1 + −2 1 1 = 3 2 6 111 0 −1 1 −2 1 1 −3t λ = −3, −2, 0 eAt [3] Find eAt where A is the matrix −2 1 −1 0 A = 1 −1 −1 0 −1 4 −2 2 000 1 1 −1 −t e 1 e −2 1 −1 + 0 1 1 + 1 1 −1 = 6 2 3 2 −1 1 011 −1 −1 1 −3t λ = −3, −1, 0 eAt [4] Find eAt where A is the matrix 2 0 −1 1 A= 0 2 −1 1 3 1 −1 1 110 1 −1 −2 2t 4t e e e −1 1 −1 + 1 1 0 + −1 1 2 = 3 2 6 1 −1 1 000 −2 2 4 t λ = 1, 2, 4 eAt [...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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