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−1
1 [6] Find eAt where A is the matrix
A= −1 −2
−2
2 + e4t
2 11
11 , 2 × 2 Exercise Set H (symmetric matrices), November λ = −2, 3 eAt = e−2t
5 42
21 + e 3t
5 + e−t
5 1 −2
−2
4 + e−t
5 4 −2
−2
1 1 −2
−2
4 [7] Find eAt where A is the matrix
A= λ = −6, −1 eAt = −5 −2
−2 −2 e−6t
5 42
21 [8] Find eAt where A is the matrix
A= λ = −6, −1 eAt = −2 −2
−2 −5 e−6t
5 12
24 , 2 × 2 Exercise Set I (quadratic forms), November 2 × 2 Exercise Set I (quadratic forms)
Linear Algebra, Dave Bayer, November , [1] Express the quadratic form
3x2 − 2xy + 3y2
as a sum of squares of othogonal linear forms. λ = 2, 4 3 −1
−1
3 A= 3x2 − 2xy + 3y2 = 11
11 = 3 −1
−1
3 xy x
y +2 1 −1
−1
1 = ( x + y) 2 + 2 ( x − y) 2 [2] Express the quadratic form
− 3x2 + 2xy − 3y2 as a sum of squares of othogonal linear forms. λ = −4, −2 −3
1
1 −3 A= − 3x2 + 2xy − 3y2 = −3
1
1 −3 xy 1 −1
−1
1 = −2
x
y − 11
11 = − 2 ( x − y ) 2 − (x + y ) 2 [3] Express the quadratic form
− x2 − 4xy − y2 as a sum of squares of...
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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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