chapter4 - Chapter 4 Solutions to 4.1 1. a) (2, 1, 3, 4) =...

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Unformatted text preview: Chapter 4 Solutions to 4.1 1. a) (2, 1, 3, 4) = (1) N(2, 1, 3, 4) = (1) 1 = 1, odd. b) (1, 3, 2, 4) = (1) N(1, 3, 2, 4) = (1) 1 = 1, odd. c) (1, 4, 3, 5, 2) = (1) N(1, 4, 3, 5, 2) = (1) 4 = 1, even. d) (5, 4, 3, 2, 1) = (1) N(5, 4, 3, 2, 1) = (1) 10 = 1, even. 3. det(A) = 1 1 2 3 = 1 3 (1)2 = 5. 5. det(A) = 1 1 2 3 6 2 1 = 1 3(1) + (1)6 0 + 0 2 2 0 3 0 6 2 1 (1)(1)2 = 17. 7. 2 2 2 = 2 2 2 2 = (2 2) 2 . 9. 3 2 6 2 1 1 1 1 4 = (3)(1)(4) + (2)(1)(1) + (6)(2)(1) (1)(1)(6) (1)(1)(3) (4)(2)(2) = 19. 11. 1/2 e 2 e 1 67 1/2 1/30 2001 2 3 = ( 1/2 )(1/30)( 3 ) + (e 2 )(2001)( ) + (e 1 )(67 1/2 )( 2 ) ( )(1/30)(e 1 ) ( 2 )(2001)( 1/2 ) ( 3 )(67 1/2 )(e 2 ) 9601.882. 116 Sec. 4.1 The Definition of a Determinant 117 13. y 1 y 1 + 4y 1 4y 1 = 8sin 2x + 4cos 2x 8sin 2x 4cos 2x = 0, y 2 y 2 + 4y 2 4y 2 = 8cos 2x + 4sin 2x + 8cos 2x 4sin 2x = 0, y 3 y 3 + 4y 3 4y 3 = e x e x + 4e x 4e x = 0. y 1 y 2 y 3 y 1 y 2 y 3 y 1 y 2 y 3 = cos 2x sin 2x e x 2sin 2x 2cos 2x e x 4cos 2x 4sin 2x e x = 2e x cos 2 2x 4e x sin 2xcos 2x + 8e x sin 2 2x + 8e x cos 2 2x + 4e x sin 2xcos 2x + 2e x sin 2 2x = 10e x . 15 . a) S 4 = {1, 2, 3, 4} N(1, 2, 3, 4) = 0, (1, 2, 3, 4) = 1; N(1, 2, 4, 3) = 1, (1, 2, 4, 3) = 1; N(1, 3, 2, 4) = 1, (1, 3, 2, 4) = 1; N(1, 3, 4, 2) = 2, (1, 3, 4, 2) = 1; N(1, 4, 2, 3) = 2, (1, 4, 2, 3) = 1; N(1, 4, 3, 2) = 3, (1, 4, 3, 2) = 1; N(2, 1, 3, 4) = 1, (2, 1, 3, 4) = 1; N(2, 1, 4, 3) = 2, (2, 1, 4, 3) = 1; N(2, 3, 1, 4) = 2, (2, 3, 1, 4) = 1; N(2, 3, 4, 1) = 3, (2, 3, 4, 1) = 1; N(2, 4, 1, 3) = 3, (2, 4, 1, 3) = 1; N(2, 4, 3, 1) = 4, (2, 4, 3, 1) = 1; N(3, 1, 2, 4) = 2, (3,1,2,4) = 1; N(3, 1, 4, 2) = 3, (3, 1, 4, 2) = 1; N(3, 2, 1, 4) = 3, (3,2,1,4) = 1; N(3, 2, 4, 1) = 4, (3, 2, 4, 1) = 1; N(3, 4, 1, 2) = 4, (3, 4, 1, 2) = 1; N(3, 4, 2, 1) = 5, (3, 4, 2, 1) = 1; N(4, 1, 2, 3) = 3, (4, 1, 2, 3) = 1; N(4, 1, 3, 2) = 4, (4, 1, 3, 2) = 1; N(4, 2, 1, 3) = 4, (4, 2, 1, 3) = 1; N(4, 2, 3, 1) = 5, (4, 2, 3, 1) = 1; N(4, 3, 1, 2) = 5, (4, 3, 1, 2) = 1; N(4, 3, 2, 1) = 6, (4, 3, 2, 1) = 1; det(A) = a 11 a 22 a 33 a 44 a 11 a 22 a 34 a 43 a 11 a 23 a 32 a 44 + a 11 a 23 a 34 a 42 + a 11 a 24 a 32 a 43 a 11 a 24 a 33 a 42 a 12 a 21 a 33 a 44 + a 12 a 21 a 34 a 43 + a 12 a 23 a 31 a 44 a 12 a 23 a 34 a 41 a 12 a 24 a 31 a 43 + a...
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chapter4 - Chapter 4 Solutions to 4.1 1. a) (2, 1, 3, 4) =...

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