Practice 4 Solutions

Where 201 a 1 1 2 102 eat 1 y 0 1 1 202 2

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Unformatted text preview: = 9 9 3 444 −4 −4 5 2 −1 −1 4t λ = 4, 1, 1 eAt [4] Find eAt where A is the matrix 110 A = 1 2 1 110 231 7 −3 −1 1 0 −1 1 t e 4 6 2 + −4 3 −2 + −1 0 1 = 9 9 3 231 −2 −3 8 1 0 −1 3t λ = 3, 0, 0 eAt [5] Find eAt where A is the matrix 220 A = 1 2 1 112 , 3 × 3 Exercise Set E (repeated roots), November 342 6 −4 −2 0 2 −2 t t e e te 3 4 2 + −3 5 −2 + 0 −1 1 = 9 9 3 342 −3 −4 7 0 −1 1 4t λ = 4, 1, 1 eAt [6] Find eAt where A is the matrix 200 A = 2 1 1 211 eAt λ = 0, 2, 2 0 0 0 200 000 2t e 1 1 −1 + 0 1 1 + te2t 2 0 0 = 0 2 2 0 −1 1 011 200 [7] Find eAt where A is the matrix 200 A = 2 1 1 111 λ = 0, 2, 2 eAt 0 0 0 400 000 2t 2t e te 1 2 −2 + 1 2 2 + 3 0 0 = −1 4 4 2 1 −2 2 −1 2 2 300 [8] Find eAt where A is the matrix 110 A = 1 2 1 102 111 3 −1 −1 −1 1 −1 t t e te e 2 2 2 + −2 2 −2 + 0 0 0 = 4 4 2 111 −1 −1 3 1 −1 1 3t λ = 3, 1, 1 eAt , 3 × 3 Exercise Set F (repeated roots), November 3 × 3 Exercise Set F (repeated roots) Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where 211 A = 1 2 1 , 001 eAt 0 y ( 0) = 1 1 111 1 −1 −1 000 t e e 1 1 1 + −1 1 −1 + tet 0 0 0 = 2 2 000 0 0 2 000 3t λ = 3, 1, 1 2 −2 0 t e e + tet 0 2+ 0 y= 2 2 0 2 0 3t [2] Solve the di erential equation y = Ay where 201 A = 1 1 2 , 102 eAt 1 y ( 0) = 1 1 202 2 0 −2 000 t t e te e 3 0 3 + −3 4 −3 + −1 0 1 = 4 4 2 202 −2 0 2 000 3t λ = 3, 1, 1 4 0 0 t t e...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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