Practice 4 Solutions

4 1 2 1 1 y 1 1 t 6 3 7 solve the di erential equation

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Unformatted text preview: di erential equation y = Ay where −1 4 , −1 −5 A= λ = −3, −3 10 01 eAt = e−3t y(0) = 2 4 −1 −2 + te−3t 1 −1 y = e−3t 1 −1 + te−3t [4] Solve the di erential equation y = Ay where 1 1 , −1 −1 A= λ = 0, 0 10 01 eAt = +t y(0) = 1 1 −1 −1 1 0 y= 1 0 +t 1 −1 [5] Solve the di erential equation y = Ay where A= λ = 0, 0 eAt = −2 −1 , 4 2 10 01 +t y(0) = −2 −1 4 2 1 −1 y= 1 −1 +t −1 2 −2 1 , 2 × 2 Exercise Set F (repeated roots), November [6] Solve the di erential equation y = Ay where 2 −4 , 1 −2 A= λ = 0, 0 10 01 eAt = +t y ( 0) = 2 −4 1 −2 1 −1 y= 1 −1 +t 6 3 [7] Solve the di erential equation y = Ay where A= λ = −1, −1 10 01 eAt = e−t −5 −4 , 4 3 + te−t y(0) = −4 −4 4 4 1 2 y = e−t 1 2 + te−t −12 12 1 2 + te−t −9 9 [8] Solve the di erential equation y = Ay where A= λ = −1, −1 eAt = e−t 10 01 −4 −3 , 3 2 + te−t y(0) = −3 −3 3 3 1 2 y = e−t , 2 × 2 Exercise Set G (symmetric matrices), November 2 × 2 Exercise Set G (symmetric matrices) Linear Algebra, Dave Bayer, November , [1] Find An where A is the matrix A= λ = −5, −1 −3 −2 −2 −3 (−5)n 2 An = 11 11 + (−1)n 2 1 −1 −1 1 [2] Find An where A is the matrix −1 2 22 A= λ = −2, 3 (−2)n 5 An = 4 −2 −2 1 3n 5 + 12 24 [3] Find An where A is the matrix A= λ = 0, 5 An = 0n 5 1 −2 −2 4 42 21 + 5n 5 1 −2 −2 4 [4] Find An where A is the matrix A= λ = −5, 0 An = −4 −2 −2 −1 (−...
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