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9
9
3
444
−4 −4
5
2 −1 −1
4t λ = 4, 1, 1 eAt [4] Find eAt where A is the matrix 110
A = 1 2 1
110 231
7 −3 −1
1 0 −1
1
t
e
4 6 2 + −4
3 −2 + −1 0
1
=
9
9
3
231
−2 −3
8
1 0 −1
3t λ = 3, 0, 0 eAt [5] Find eAt where A is the matrix 220
A = 1 2 1
112 , 3 × 3 Exercise Set E (repeated roots), November 342
6 −4 −2
0
2 −2
t
t
e
e
te 3 4 2 +
−3
5 −2 +
0 −1
1
=
9
9
3
342
−3 −4
7
0 −1
1
4t λ = 4, 1, 1 eAt [6] Find eAt where A is the matrix 200
A = 2 1 1
211 eAt λ = 0, 2, 2 0
0
0
200
000
2t
e
1
1 −1 +
0 1 1 + te2t 2 0 0 = 0
2
2
0 −1
1
011
200 [7] Find eAt where A is the matrix 200
A = 2 1 1
111 λ = 0, 2, 2 eAt 0
0
0
400
000
2t
2t
e
te 1
2 −2 +
1 2 2 +
3 0 0
= −1
4
4
2
1 −2
2
−1 2 2
300 [8] Find eAt where A is the matrix 110
A = 1 2 1
102 111
3 −1 −1
−1
1 −1
t
t
e
te e
2 2 2 +
−2
2 −2 +
0
0
0
=
4
4
2
111
−1 −1
3
1 −1
1
3t λ = 3, 1, 1 eAt , 3 × 3 Exercise Set F (repeated roots), November 3 × 3 Exercise Set F (repeated roots)
Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where 211
A = 1 2 1 ,
001 eAt 0
y ( 0) = 1 1 111
1 −1 −1
000
t
e
e
1 1 1 +
−1
1 −1 + tet 0 0 0 =
2
2
000
0
0
2
000
3t λ = 3, 1, 1 2
−2
0
t
e
e + tet 0 2+
0
y=
2
2
0
2
0
3t [2] Solve the di erential equation y = Ay where 201
A = 1 1 2 ,
102 eAt 1
y ( 0) = 1 1 202
2 0 −2
000
t
t
e
te e
3 0 3 +
−3 4 −3 +
−1 0 1 =
4
4
2
202
−2 0
2
000
3t λ = 3, 1, 1 4
0
0
t
t
e...
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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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