Practice 4 Solutions

2 000 001 1 21 eat 4 1 1 2t t tet 1 t e 2 1 ye 2 0 0

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Unformatted text preview: −2 12 2 λ = 2, 2, 2 4 4 −4 100 02 2 2 2t te −2 −2 2 = e2t 0 1 0 + te2t 1 0 −2 + 2 2 2 −2 001 12 0 eAt [7] Find eAt where A is the matrix 3 2 2 A = −2 −1 −2 −2 −2 1 λ = 1, 1, 1 −4 −4 0 100 2 2 2 2t te 4 4 0 = et 0 1 0 + tet −2 −2 −2 + 2 0 00 001 −2 −2 0 eAt [8] Find eAt where A is the matrix 2 −2 −2 2 1 A = −1 2 2 2 , 3 × 3 Exercise Set H (identical roots), November λ = 2, 2, 2 −2 −4 −2 100 0 −2 −2 2 2t te 2 4 2 0 1 + = e2t 0 1 0 + te2t −1 2 −2 −4 −2 001 2 2 0 eAt , 3 × 3 Exercise Set I (identical roots), November 3 × 3 Exercise Set I (identical roots) Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where −1 3 1 A = −1 2 1 , −1 1 2 1 y(0) = 1 0 λ = 1, 1, 1 0 −2 2 100 −2 3 1 t2 et 0 −1 1 = et 0 1 0 + tet −1 1 1 + 2 0 −1 1 001 −1 1 1 eAt −2 1 1 2t te −1 y = et 1 + tet 0 + 2 0 −1 0 [2] Solve the di erential equation y = Ay where 2 −2 −2 2 −2 , A= 2 −1 −1 2 1 y ( 0) = 1 0 λ = 2, 2, 2 −2 2 4 100 0 −2 −2 2 2t te 0 −2 + 2 −2 −4 = e2t 0 1 0 + te2t 2 2 −2 2 4 001 −1 −1 0 eAt 0 1 −2 2 2t 2t + te2t 2 + t e 0 1 y=e 2 0 0 −2 [3] Solve the di erential equation y = Ay where 1 −1 −1 A = −1 −2 −2 , 2 1 1 λ = 0, 0, 0 2 y ( 0) = 0 1 , 3 × 3 Exercise Set I (identical roots), November 100 0 0 0 1 −1 −1 2 t −3 3 3 = 0 1 0 + t −1 −2 −2 + 2 001 3 −3 −3 2 1 1 eAt 0 2 1 t2 −3 y = 0 + t −4 + 2 3 1 5 [4] Solve the...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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