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Unformatted text preview: −2 12
2
λ = 2, 2, 2 4
4 −4
100
02
2
2 2t
te −2 −2
2
= e2t 0 1 0 + te2t 1 0 −2 +
2
2
2 −2
001
12
0 eAt [7] Find eAt where A is the matrix 3
2
2
A = −2 −1 −2 −2 −2
1
λ = 1, 1, 1 −4 −4 0
100
2
2
2
2t
te 4
4 0
= et 0 1 0 + tet −2 −2 −2 +
2
0
00
001
−2 −2
0 eAt [8] Find eAt where A is the matrix 2 −2 −2
2
1
A = −1
2
2
2 , 3 × 3 Exercise Set H (identical roots), November
λ = 2, 2, 2 −2 −4 −2
100
0 −2 −2
2 2t
te 2
4
2
0
1 +
= e2t 0 1 0 + te2t −1
2
−2 −4 −2
001
2
2
0 eAt , 3 × 3 Exercise Set I (identical roots), November 3 × 3 Exercise Set I (identical roots)
Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where −1 3 1
A = −1 2 1 ,
−1 1 2 1
y(0) = 1 0 λ = 1, 1, 1 0 −2 2
100
−2 3 1
t2 et 0 −1 1 = et 0 1 0 + tet −1 1 1 +
2
0 −1 1
001
−1 1 1 eAt −2
1
1
2t
te −1 y = et 1 + tet 0 +
2
0
−1
0 [2] Solve the di erential equation y = Ay where 2 −2 −2
2 −2 ,
A= 2
−1 −1
2 1
y ( 0) = 1 0 λ = 2, 2, 2 −2
2
4
100
0 −2 −2
2 2t
te 0 −2 +
2 −2 −4 = e2t 0 1 0 + te2t 2
2
−2
2
4
001
−1 −1
0 eAt 0
1
−2
2 2t
2t + te2t 2 + t e 0 1
y=e
2
0
0
−2 [3] Solve the di erential equation y = Ay where 1 −1 −1
A = −1 −2 −2 ,
2
1
1 λ = 0, 0, 0 2
y ( 0) = 0 1 , 3 × 3 Exercise Set I (identical roots), November 100
0
0
0
1 −1 −1
2
t
−3
3
3
= 0 1 0 + t −1 −2 −2 +
2
001
3 −3 −3
2
1
1 eAt 0
2
1
t2 −3 y = 0 + t −4 +
2
3
1
5 [4] Solve the...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.
 Spring '14
 DaveBayer
 Linear Algebra, Algebra

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