Unformatted text preview: −2
−2
3 =− 0 −2
−2
3 x
y 1
5 42
21 =− + 4
5 1 −2
−2
4 4
1
( 2x + y ) 2 +
( x − 2y ) 2
5
5 , Final Exam, December
[6] Solve the recurrence relation
f(0) = a, f(n + 1)
f(n) = f(1) = b, 3 −2
1
0 n b
a f(n) = 3 f(n − 1) − 2 f(n − 2) = −1 2
−1 2 b
a + 2n f(n) = ( − b + 2a) + 2n (b − a) 2 −2
1 −1 b
a , Final Exam, December
[7] Find eAt where A is the matrix 121
A = 0 2 0
121 λ = 0, 2, 2 eAt 1 0 −1
101
020
2t
1
e
0 +
0 2 0 + te2t 0 0 0 = 00
2
2
−1 0
1
101
020 , Final Exam, December
[8] Solve the di erential equation y = Ay where −2 2 −1
A = −1 1 −2 ,
−1 1
1 2
y(0) = 0 1 λ = 0, 0, 0 3 −3 −3
100
−2 2 −1
2
t
3 −3 −3 = 0 1 0 + t −1 1 −2 +
2
0
0
0
001
−1 1
1 eAt 3
2
−5
t2 3
y = 0 + t −4 +
2
0
1
−1 ,...
View
Full
Document
This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.
 Spring '14
 DaveBayer
 Linear Algebra, Algebra

Click to edit the document details