Practice 4 Solutions

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 (−...
View Full Document

Ask a homework question - tutors are online