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λ = 1, 1, 1 3 −3 3
100
−2
21
n(n − 1) 3 −3 3 1 2 +
= 0 1 0 + n −1
2
0
00
001
1 −1 1 An [8] Find An where A is the matrix 2 −2 −1
2 −1 A= 2
−2 −2
2 , 3 × 3 Exercise Set G (identical roots), November
λ = 2, 2, 2 −2
2
2
100
0 −2 −1
n−2
n(n − 1) 2 2 −2 −2 0 −1 +
= 2n 0 1 0 + n 2n−1 2
2
−4
4
4
001
−2 −2
0 An , 3 × 3 Exercise Set H (identical roots), November 3 × 3 Exercise Set H (identical roots)
Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix 23
3
A = 1 1 −1 −1 1
3
λ = 2, 2, 2 0
0
0
100
0
3
3
2 2t
te 0
3
3
= e2t 0 1 0 + te2t 1 −1 −1 +
2
0 −3 −3
001
−1
1
1 eAt [2] Find eAt where A is the matrix −2
22
1 3
A = −1
1 −1 1
λ = 0, 0, 0 4 −4 4
100
−2
22
2
t
4 −4 4 1 3 +
= 0 1 0 + t −1
2
0
00
001
1 −1 1 eAt [3] Find eAt where A is the matrix −1 3
2
A = 2 1 −2 −2 3
3
λ = 1, 1, 1 100
−2 3
2
6 0 −6
2t
te 00
0
= et 0 1 0 + tet 2 0 −2 +
2
6 0 −6
001
−2 3
2 eAt [4] Find eAt where A is the matrix −2
2
2
1
A = 1 −2
−2
2 −2
λ = −2, −2, −2 , 3 × 3 Exercise Set H (identical roots), November −2
4
2
100
022
2 −2t
te −2
4
2
= e−2t 0 1 0 + te−2t 1 0 1 +
2
2 −4 −2
001
−2 2 0 eAt [5] Find eAt where A is the matrix −2 −1 1
A = −1 −2 3 −1 −1 1
λ = −1, −1, −1 eAt 1
1 −2
100
−1 −1 1
2 −t
te −1 −1
2
= e−t 0 1 0 + te−t −1 −1 3 +
2
0
0
0
001
−1 −1 2 [6] Find eAt where A is the matrix 22
2
A = 1 2...
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 Spring '14
 DaveBayer
 Linear Algebra, Algebra

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