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Unformatted text preview: 2, 4 An 1 −1 −1
110
1 −1
2
n
n
1
2
4
1
1 +
1 1 0 +
−1
1 −2 = −1
3
2
6
−1
1
1
000
2 −2
4 3 × 3 Exercise Set K (symmetric matrices), November , 3 × 3 Exercise Set K (symmetric matrices)
Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix −3
1
0
A = 1 −2 −1 0 −1 −3 1 −1 −1
101
1
2 −1
−3t
−t
e
e −1
0 0 0 + e 2
1
1 +
4 −2 =
3
2
6
−1
1
1
101
−1 −2
1
−4t λ = −4, −3, −1 eAt [2] Find eAt where A is the matrix −1 −1 −1
0
A = −1 −2
−1
0 −2 111
0
0
0
4 −2 −2
−2t
1
e
1 1 1 + e
0
1 −1 + −2
1
1
=
3
2
6
111
0 −1
1
−2
1
1
−3t λ = −3, −2, 0 eAt [3] Find eAt where A is the matrix −2
1 −1
0
A = 1 −1
−1
0 −1 4 −2
2
000
1
1 −1
−t
e
1
e −2
1 −1 +
0 1 1 + 1
1 −1 =
6
2
3
2 −1
1
011
−1 −1
1
−3t λ = −3, −1, 0 eAt [4] Find eAt where A is the matrix 2 0 −1
1
A= 0 2
−1 1
3 1 −1
1
110
1 −1 −2
2t
4t
e
e
e
−1
1 −1 +
1 1 0 +
−1
1
2
=
3
2
6
1 −1
1
000
−2
2
4
t λ = 1, 2, 4 eAt [...
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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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