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Unformatted text preview: −2
1
−1 0
1
111
n An λ = 0, 2, 3 [2] Find An where A is the matrix −3
1 −1
0
A = 1 −2
−1
0 −2 λ = −4, −2, −1 An 4 −2
2
000
1
1 −1
(−2)n (−1)n (−4)n −2
1 −1 +
0 1 1 +
1
1 −1 =
6
2
3
2 −1
1
011
−1 −1
1 [3] Find An where A is the matrix 2 1 −1
0
A= 1 1
−1 0
1 λ = 0, 1, 3 An 1 −1
1
000
4
2 −2
0n 1
3n −1
1 −1 +
0 1 1 +
2
1 −1 =
3
2
6
1 −1
1
011
−2 −1
1 [4] Find An where A is the matrix 3 −1 0
2 1
A = −1
0
13 λ = 1, 3, 4 An 1
2 −1
101
1 −1 −1
3n 4n 1
2
4 −2 +
0 0 0 +
−1
1
1
=
6
2
3
−1 −2
1
101
−1
1
1 [5] Find An where A is the matrix −2
1
0
A = 1 −3 −1 0 −1 −2 3 × 3 Exercise Set J (symmetric matrices), November 1 −2 −1
101
1
1 −1
n
n
(−4) (−2) (−1) −2
4
2 +
0 0 0 +
1
1 −1 =
6
2
3
−1
2
1
101
−1 −1
1
n λ = −4, −2, −1 , An [6] Find An where A is the matrix −1
0 −1
1
A = 0 −1
−1
1 −2 1 −1
2
110
1 −1 −1
n
n
(−1) 0
(−3) −1
1 −2 +
1 1 0 +
−1
1
1
=
6
2
3
2 −2
4
000
−1
1
1
n λ = −3, −1, 0 An [7] Find An where A is the matrix 3 0 −1
1
A= 0 3
−1 1
2 λ = 1, 3, 4 An 1 −1
2
110
1 −1 −1
n
n
3
4
1
1 −2 +
1 1 0 +
−1
1
1
= −1
6
2
3
2 −2
4
000
−1
1
1 [8] Find An where A is the matrix 2
0
1
2 −1 A = 0
1 −1
3 λ = 1,...
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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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