Practice 4 Solutions

2 2 te2t 1 1 1 1 4 find eat where a is the matrix a

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Unformatted text preview: n −5 −4 1 −1 10 01 + n (−3)n−1 −2 −4 1 2 , 2 × 2 Exercise Set E (repeated roots), November 2 × 2 Exercise Set E (repeated roots) Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix A= 5 −4 4 −3 eAt = et 10 01 A= −5 −4 4 3 eAt = e−t 10 01 A= λ = 1, 1 −3 −1 1 −1 eAt = e−2t 10 01 + tet 4 −4 4 −4 [2] Find eAt where A is the matrix λ = −1, −1 −4 −4 4 4 + te−t [3] Find eAt where A is the matrix λ = −2, −2 + te−2t −1 −1 1 1 [4] Find eAt where A is the matrix A= λ = 4, 4 eAt = e4t 51 −1 3 10 01 + te4t 1 1 −1 −1 [5] Find eAt where A is the matrix A= λ = 0, 0 eAt = 1 1 −1 −1 10 01 [6] Find eAt where A is the matrix A= −4 3 −3 2 +t 1 1 −1 −1 , 2 × 2 Exercise Set E (repeated roots), November λ = −1, −1 eAt = e−t 10 01 + te−t −3 3 −3 3 [7] Find eAt where A is the matrix A= 3 −2 2 −1 eAt = et 10 01 A= λ = 1, 1 −1 2 −2 −5 eAt = e−3t 10 01 + tet 2 −2 2 −2 [8] Find eAt where A is the matrix λ = −3, −3 + te−3t 2 2 −2 −2 , 2 × 2 Exercise Set F (repeated roots), November 2 × 2 Exercise Set F (repeated roots) Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where 5 4 , −4 −3 A= 10 01 eAt = et λ = 1, 1 + tet y(0) = 4 4 −4 −4 1 1 y = et 1 1 + tet 8 −8 [2] Solve the di erential equation y = Ay where A= λ = 4, 4 2 −4 , 1 6 10 01 + te4t eAt = e4t y(0) = −2 −4 1 2 2 1 y = e 4t 2 1 + te4t −8 4 [3] Solve the...
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