Unformatted text preview: eAt where A is the matrix 221
A = 0 2 1
012 0 −1
1
033
1 −1 −2
3t
e
e
0
1 −1 + e2t 0
0 1 1
0
0 +
=
2
2
0 −1
1
011
0
0
0
t λ = 1, 2, 3 eAt [8] Find eAt where A is the matrix 120
A = 1 0 1
112 1 −3
1
1
1 −1
111
t
3t
e
e
e
−1
3 −1 +
0
0
0 +
1 1 1
=
4
2
4
0
0
0
−1 −1
1
222
−t λ = −1, 1, 3 eAt , 3 × 3 Exercise Set C (distinct roots), November 3 × 3 Exercise Set C (distinct roots)
Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where 120
A = 1 1 2 ,
011 eAt 0
y ( 0) = 1 1 2 −4
4
2 0 −4
244
t
3t
e
e
e
−2
4 −4 +
00
0 +
2 4 4
=
8
4
8
1 −2
2
−1 0
2
122
−t λ = −1, 1, 3 0
−4
8
t
3t
e
e + e 8
0+
0
y=
8
4
8
0
2
4
−t [2] Solve the di erential equation y = Ay where 222
A = 0 2 0 ,
121 2
y ( 0) = 0 1 λ = 0, 2, 3 eAt 1
1 −2
282
0 −3 0
3t
e
1
0
0 + e 2t 0
0 0 0
1 0 +
= 0
3
3
−1 −1
2
141
0 −1 0 0
6
0
3t
1 2t + e 0
0 +e
0
y=
3
3
0
3
0 [3] Solve the di erential equation y = Ay where 210
A = 2 2 1 ,
022 2
y ( 0) = 0 1 λ = 0, 2, 4 eAt 2 −2
1
2 0 −1
221
2t
4t
1
e
e
4 −2 +
00
0 +
4 4 2
= −4
8
4
8
4 −4
2
−4 0
2
442 5
3
5
2t
4t
1
e
e
0 +
10 y = −10 +
8
4
8
10
−6
10 , 3 × 3 Exercise Set C (distinct roots), November
[4] Solve the di erential equation y = Ay where 200
A = 2 2 1 ,
221 2
y ( 0) = 0 1 λ = 0, 2, 3 eAt 0
0
0
000
100
3t
1
e
1 −1 + e2t −2 0 0 +
6 2 1
= 0
3
3
0 −2
2
621
−2 0 0 0
0
2
3t
e
1
13 y = −1 + e2t −4 +
3
3
2
13
−4 [5] Solve the di erential equation y =...
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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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