AEM_3e_Chapter_08

AEM_3e_Chapter_08 - 8 8 Matrices EXERCISES 8.1 Matrix...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 8 8 Matrices EXERCISES 8.1 Matrix Algebra 3. 3 3 6. 8 1 9. Not equal 12. Solving x 2 = 9, y = 4 x we obtain x = 3, y = 12 and x = 3, t = 12. 15. (a) A + B = 4 2 5 + 6 6 + 8 9 10 = 2 11 2 1 (b) B A = 2 4 6 5 8 + 6 10 9 = 6 1 14 19 (c) 2 A + 3 B = 8 10 12 18 + 6 1 8 24 30 = 2 2 8 12 12 18. (a) AB = 4 + 4 6 12 3 + 8 20 + 10 30 30 15 + 20 32 + 12 48 36 24 + 24 = 6 5 10 0 5 20 12 0 (b) BA = 4 + 30 24 16 + 60 36 1 15 + 16 4 30 + 24 = 2 8 2 2 21. (a) A T A = (4 8 10) 4 8 10 = (180) (b) B T B = 2 4 5 (2 4 5) = 4 8 10 8 16 20 10 20 25 (c) A + B T = 4 8 10 + 2 4 5 = 6 12 5 24. (a) A T + B = 5 4 9 6 + 3 11 7 2 = 2 7 2 8 (b) 2 A + B T = 10 18 8 12 + 3 7 11 2 = 7 11 3 14 113 8.1 Matrix Algebra 27. 19 18 19 20 = 38 2 30. 3 2 33. ( AB ) T = 16 40 8 20 T = 16 8 40 20 ; B T A T = 4 2 10 5 2 3 4 2 = 16 8 40 20 36. Using the property ( AB ) T = B T A T given in Problem 33 we have ( AA T ) T = ( A T ) T A T = AA T , so that AA T is symmetric. 39. Since ( A + B ) 2 = ( A + B )( A + B ) 6 = A 2 + AB + BA + B 2 , and AB 6 = BA in general, ( A + B ) 2 6 = A 2 +2 AB + B 2 . 42. 2 6 1 1 2 1 5 7 4 x 1 x 2 x 3 = 7 1 9 45. (a) M Y x y z = cos sin sin cos 1 x y z = x cos + y sin x sin + y cos z = x Y y Y z Y (b) M R = cos sin 1 sin cos ; M P 1 cos sin sin cos (c) M P 1 1 1 = 1 cos30 sin30 sin30 cos30 1 1 1 = 1 3 2 1 2 1 2 3 2 1 1 1 = 1 1 2 ( 3 + 1) 1 2 ( 3 1) M R M P 1 1 1 = cos45 sin45 1 sin45 cos45 1 1 2 ( 3 + 1) 1 2 ( 3 1) = 2 2 2 2 1 2 2 2 2 1 1 2 ( 3 + 1) 1 2 ( 3 1) = 1 4 (3 2 6) 1 2 ( 3 + 1) 1 4 ( 2 + 6) M Y M R M P 1 1 1 = cos60 sin60 sin60 cos60 1 1 4 (3 2 6) 1 2 ( 3 + 1) 1 4 ( 2 + 6)...
View Full Document

Page1 / 24

AEM_3e_Chapter_08 - 8 8 Matrices EXERCISES 8.1 Matrix...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online