Unformatted text preview: n −5 −4
1 −1 10
01 + n (−3)n−1 −2 −4
1
2 , 2 × 2 Exercise Set E (repeated roots), November 2 × 2 Exercise Set E (repeated roots)
Linear Algebra, Dave Bayer, November , [1] Find eAt where A is the matrix
A= 5 −4
4 −3 eAt = et 10
01 A= −5 −4
4
3 eAt = e−t 10
01 A= λ = 1, 1 −3 −1
1 −1 eAt = e−2t 10
01 + tet 4 −4
4 −4 [2] Find eAt where A is the matrix λ = −1, −1 −4 −4
4
4 + te−t [3] Find eAt where A is the matrix λ = −2, −2 + te−2t −1 −1
1
1 [4] Find eAt where A is the matrix
A= λ = 4, 4 eAt = e4t 51
−1 3
10
01 + te4t 1
1
−1 −1 [5] Find eAt where A is the matrix
A= λ = 0, 0 eAt = 1
1
−1 −1
10
01 [6] Find eAt where A is the matrix
A= −4 3
−3 2 +t 1
1
−1 −1 , 2 × 2 Exercise Set E (repeated roots), November λ = −1, −1 eAt = e−t 10
01 + te−t −3 3
−3 3 [7] Find eAt where A is the matrix
A= 3 −2
2 −1 eAt = et 10
01 A= λ = 1, 1 −1
2
−2 −5 eAt = e−3t 10
01 + tet 2 −2
2 −2 [8] Find eAt where A is the matrix λ = −3, −3 + te−3t 2
2
−2 −2 , 2 × 2 Exercise Set F (repeated roots), November 2 × 2 Exercise Set F (repeated roots)
Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where
5
4
,
−4 −3 A= 10
01 eAt = et λ = 1, 1 + tet y(0) = 4
4
−4 −4 1
1 y = et 1
1 + tet 8
−8 [2] Solve the di erential equation y = Ay where
A= λ = 4, 4 2 −4
,
1
6 10
01 + te4t eAt = e4t y(0) = −2 −4
1
2 2
1 y = e 4t 2
1 + te4t −8
4 [3] Solve the...
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 Spring '14
 DaveBayer
 Linear Algebra, Algebra

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