Practice 4 Solutions

1 000 t e e 0 1 1 0 1 1 tet 0 0 0 2 2 011 0 1 1 000

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Unformatted text preview: 202 2 0 −2 00 0 3n 1 n 3 0 3 + −3 4 −3 + 1 0 −1 = 4 4 2 202 −2 0 2 00 0 [4] Find An where A is the matrix 211 A = 2 2 0 112 λ = 4, 1, 1 An 432 5 −3 −2 −1 0 1 1 n 4n 4 3 2 + −4 6 −2 + 2 0 −2 = 9 9 3 432 −4 −3 7 −1 0 1 [5] Find An where A is the matrix 222 A = 1 2 1 012 , 3 × 3 Exercise Set D (repeated roots), November 366 6 −6 −6 0 0 0 4 1 n 2 4 4 + −2 5 −4 + 1 −1 −1 = 9 9 3 122 −1 −2 7 −1 1 1 n λ = 4, 1, 1 An [6] Find An where A is the matrix 100 A = 1 2 1 112 000 2 0 0 000 1 3 1 1 1 + −1 1 −1 + n 0 0 0 = 2 2 111 −1 −1 1 000 n λ = 3, 1, 1 An [7] Find An where A is the matrix 211 A = 1 2 0 222 442 5 −4 −2 −1 −1 1 1 n 4 2 2 1 + −2 7 −1 + 1 1 −1 = 9 9 3 663 −6 −6 6 0 0 0 n λ = 4, 1, 1 An [8] Find An where A is the matrix 201 A = 1 2 1 011 111 3 −1 −1 1 −1 1 3 1 n 2 2 2 + −2 2 −2 + 0 0 0 = 4 4 2 111 −1 −1 3 −1 1 −1 n λ = 3, 1, 1 An , 3 × 3 Exercise Set E (repeated roots), November 3 × 3 Exercise Set E (repeated roots) Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix 100 A = 1 2 1 212 000 4 0 0 000 t t e e te 3 2 2 + −3 2 −2 + −1 0 0 = 4 4 2 322 −3 −2 2 100 3t λ = 3, 1, 1 eAt [2] Find eAt where A is the matrix 111 A = 0 2 1 012 011 2 −1 −1 000 t e e 0 1 1 + 0 1 −1 + tet 0 0 0 = 2 2 011 0 −1 1 000 3t eAt λ = 3, 1, 1 [3] Find eAt where A is the matrix 211 A = 0 2 1 212 333 6 −3 −3 0 0 0 t t e te e 2 2 2 + −2 7 −2 + −2 1 1...
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