Practice 4 Solutions

0 1 3 0 0 0 200 000 t 3t 1 e e 1 1 1 0 0 5 4 2

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Unformatted text preview: 00 2 000 n λ = 0, 2, 3 An [7] Find An where A is the matrix 111 A = 0 1 0 222 2 0 −1 0 −1 0 232 n 1 3 0 00 0 + 0 2 0 + 0 0 0 = 3 2 6 −2 0 1 0 −2 0 464 n λ = 0, 1, 3 An [8] Find An where A is the matrix 200 A = 2 2 2 211 0 0 0 000 100 n 0 3 1 1 −2 + 2n −3 0 0 + 8 2 2 = 3 3 −1 −1 2 411 −1 0 0 n λ = 0, 2, 3 An , 3 × 3 Exercise Set B (distinct roots), November 3 × 3 Exercise Set B (distinct roots) Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix 211 A = 2 1 2 002 λ = 0, 2, 3 eAt 2 −2 1 0 0 −3 214 2t 3t 1 e e 4 −2 + 0 0 −2 + 2 1 4 = −4 6 2 3 0 0 0 00 2 000 [2] Find eAt where A is the matrix 212 A = 0 1 1 110 1 1 −3 1 −3 −1 555 t 3t e e e 1 1 −3 + −1 3 1 + 1 1 1 = 8 4 8 −2 −2 6 0 0 0 222 −t λ = −1, 1, 3 eAt [3] Find eAt where A is the matrix 112 A = 1 2 1 100 3 −1 −5 1 −1 1 333 t 3t e e e 0 0 0 + −2 2 −2 + 4 4 4 = 8 4 8 −3 1 5 1 −1 1 111 −t λ = −1, 1, 3 eAt [4] Find eAt where A is the matrix 012 A = 1 1 1 102 6 −3 −3 0 1 −1 215 t 3t e e e −2 1 1 + 0 3 −3 + 2 1 5 = 8 4 8 −2 1 1 0 −1 1 215 −t λ = −1, 1, 3 eAt [5] Find eAt where A is the matrix 100 A = 2 2 1 121 , 3 × 3 Exercise Set B (distinct roots), November λ = 0, 1, 3 0 0 0 200 000 t 3t 1 e e 1 −1 + −1 0 0 + 5 4 2 = −1 3 2 6 2 −2 2 −3 0 0 542 eAt [6] Find eAt where A is the matrix 221 A = 0 1 0 221 λ = 0, 1, 3 eAt 1 0 −1 231 0 −1 0 3t 1 e 0 + et 0 0 0 0 1 0 + = 00 3 3 −2 0 2 231 0 −1 0 [7] Find...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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