Practice 4 Solutions

4 2 3 1 1 3 a 3x2 2xy 3y2 3 1 1 3 xy 1 1 1 1

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Unformatted text preview: −1 −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.

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