Practice 4 Solutions

# 1 3 1 1 1 n 3 1 1 an 2 find an where a is the matrix

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: Ay where 220 A = 1 1 0 , 211 λ = 0, 1, 3 eAt 1 y ( 0) = 1 1 1 −2 0 0 00 440 et e 3t 1 −1 2 0 + 0 0 0 + 2 2 0 = 3 2 6 −1 20 −1 −3 2 550 −1 0 8 t 3t 1 e e 0 + 4 y = 1 + 3 2 6 1 −2 10 [6] Solve the di erential equation y = Ay where 220 A = 1 1 0 , 111 0 y ( 0) = 1 1 λ = 0, 1, 3 eAt 1 −2 0 0 00 440 t 3t e e 1 2 0 + 0 0 0 + 2 2 0 = −1 3 2 6 0 00 −1 −1 2 330 −2 0 4 t 3t 1 + e 0 + e 2 2 y= 3 2 6 0 1 3 [7] Solve the di erential equation y = Ay where 210 A = 0 1 1 , 221 1 y ( 0) = 1 1 , 3 × 3 Exercise Set C (distinct roots), November λ = 0, 1, 3 eAt −1 −1 1 2 0 −1 221 t 3t 1 e e 2 −2 + −2 0 1 + 2 2 1 = 2 3 2 6 −2 −2 2 00 0 442 −1 1 5 t 3t 1 e e −1 + 5 y = 2 + 3 2 6 −2 0 10 [8] Solve the di erential equation y = Ay where 111 A = 0 2 1 , 111 0 y ( 0) = 1 1 λ = 0, 1, 3 eAt 1 0 −1 1 −1 0 132 t 3t e e 1 −1 1 0 + 1 3 2 = 1 0 −1 + 3 2 6 −2 0 2 1 −1 0 132 −1 −1 5 t 3t 1 e e 1 + 5 y = −1 + 3 2 6 2 −1 5 , 3 × 3 Exercise Set D (repeated roots), November 3 × 3 Exercise Set D (repeated roots) Linear Algebra, Dave Bayer, November , [1] Find An where A is the matrix 211 A = 1 1 0 012 222 2 −2 −2 0 0 0 3 1 n 1 1 1 + −1 3 −1 + 1 −1 −1 = 4 4 2 111 −1 −1 3 −1 1 1 n λ = 3, 1, 1 An [2] Find An where A is the matrix 211 A = 0 2 1 212 λ = 4, 1, 1 An 333 6 −3 −3 0 0 0 1 n 4n 2 2 2 + −2 7 −2 + −2 1 1 = 9 9 3 444 −4 −4 5 2 −1 −1 [3] Find An where A is the matrix 201 A = 2 1 1 102 λ = 3, 1, 1 An...
View Full Document

Ask a homework question - tutors are online