# chapter3 - i book 2005/4/7 22:31 page S-11#32 i i i Answers...

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± ± “book” — 2005/4/7 — 22:31 — page S-11 — #32 ± ± ± ± Answers to Selected Exercises for Chapter 3 Section 3.0 (page 148) 1. (a) · 618 6 16 ¸ (b) operation not defned because matrices do not have same dimensions 3. (a) 8 42 2 1 34 6 2 14 (b) · 7 9 18 16 ¸ 5. (a) 11 3 5 25 21 17 (b) operation not defned because the number oF columns in C is not equal to the number oF rows in B 7. (a) 6 (b) operation not defned because A is not a square matrix 9. (a) 18 6 17 5 4 30 (b) 3 45 111 057 11. No. IF A is and n × m matrix, then A T is an m × n matrix. With n ± = m ,an n × m matrix can never be equal to an m × n matrix. Section 3.1 (page 157) 1. x = £ 11 2 ¤ T 3. x = £ 112 ¤ T 5. x = £ 1111 ¤ T 7. n 2 n additional arithmetic operations 9. (a) The number oF arithmetic operations is given by n 1 ± i =1 n ± j = i +1 ² 1+ 2 n ± k = i +1 2 + n ± i =2 i 1 ± j =1 ² 2 n ± k = i +1 2 + n 2 (b) The number oF arithmetic operations is given by n 1 ± i =1 n ± j = i +1 ² n + i 1 ± k = i +1 2 + n ± i =2 i 1 ± j =1 ² n + i 1 ± k = i +1 2 + n 2 S-11

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± ± “book” — 2005/4/7 — 22:31 — page S-12 — #33 ± ± ± ± S-12 Answers to Selected Exercises for Chapter 3 11. (a) x = £ 3 . 7 1 . 9 7 . 0 ¤ T (b) x = £ 3 . 707415 1 . 914830 7 . 037074 ¤ T (c) x = £ 3 . 679 1 . 873 6 . 94 ¤ T 13. I 1 =6 . 88 ,I 2 =4 . 80 3 =2 . 08 15. g = £ 0 . 00472 3 . 84552 0 . 71974 0 . 12518 ¤ T Section 3.2 (page 168) 1. (a) no pivoting: row 2, column 1; partial pivoting: row 2, column 1; scaled partial pivoting: row 2, column 1 (b) no pivoting: row 1, column 1; partial pivoting: row 4, column 1; scaled partial pivoting: row 1, column 1 (c) no pivoting: row 1, column 1; partial pivoting: row 2, column 1; scaled partial pivoting: row 3, column 1 (d) no pivoting: row 1, column 1; partial pivoting: row 1, column 1; scaled partial pivoting: row 2, column 1 (e) no pivoting: row 1, column 1; partial pivoting: row 3, column 1; scaled partial pivoting: row 4, column 1 3. no pivoting 3 13 1 6 02 3 4 1 0 42 9 7 01 6 24 43 51 partial pivoting 0 2 3 1 43 24 17 8 0 2 3 5 5 12 21 4 0 4 3 2 11 6 3 2 72 8 48 19 93 , r = 4 2 3 1 scaled partial pivoting 3 1 6 4 1 0 9 7 6 24 43 51 , r = 1 2 3 4 , s = 3 9 12 72 5. no pivoting 0 . 25 0 . 35 0 . 15 0 . 60 0 0 . 08 0 . 13 0 . 42 0 0 . 01 0 . 16 0 . 34 partial pivoting 0 . 25 0 . 35 0 . 15 0 . 60 0 0 . 08 0 . 13 0 . 42 0 0 . 01 0 . 16 0 . 34 , r = 1 2 3 scaled partial pivoting 00 . 10 0 . 1625 0 . 525 0 . 20 0 . 20 0 . 25 0 . 90 . 05 0 . 0625 0 . 025 , r = 2 1 3 , s = 0 . 35 0 . 25 0 . 25
± ± “book” — 2005/4/7 — 22:31 — page S-13 — #34 ± ± ± ± Selected answers for Section 3.2 S-13 7. x = £ 2 31 ¤ T (a) 231 4 414 9 346 0 0 5 2 1 17 2 41 4 9 0 13 4 3 27 4 00 43 13 43 13 9 0 13 4 3 27 4 r = £ 123 ¤ T r = £ 213 ¤ T r = £ ¤ T (b) 4 9 0 0 5 2 1 17 2 9 0 13 4 3 27

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chapter3 - i book 2005/4/7 22:31 page S-11#32 i i i Answers...

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