경문사 선형대수학david c lay 3rd 판 솔루션 (구매자 판매중지)

1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 19?22, and 25. For brevity, the symbols R1, R2,…, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 ?2 x1 ? 7 x2 = ?5 ? 1 ? ?2 ? 5 ?7 7? ?5? ? x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 ?1 ?0 ? ?1 ?0 ? ?1 ?0 ? 5 3 5 1 0 1 7? 9? ? 7? 3? ? ?8? 3? ? Scale R2 by 1/3: Replace R1 by R1 + (?5)R2: The solution is (x1, x2) = (?8, 3), or simply (?8, 3). 2. = ?8 x2 = 3 2 x1 + 4 x2 = ?4 5 x1 + 7 x2 = 11 ?2 ?5 ? 4 7 ?4 ? 11 ? ? x1 + 2 x2 = ?2 Scale R1 by 1/2 and obtain: Replace R2 by R2 + (?5)R1: Scale R2 by ?1/3: Replace R1 by R1 + (?2)R2: The solution is (x1, x2) = (12, ?7), or simply (12, ?7). 5 x1 + 7 x2 = 11 x1 + 2 x2 = ?2 ?1 ?5 ? ?1 ?0 ? ?1 ?0 ? ?1 ?0 ? 2 7 2 ?3 2 1 0 1 ?2 ? 11 ? ? ?2 ? 21? ? ?2 ? ?7 ? ? 12 ? ?7 ? ? ?3x2 = 21 x1 + 2 x2 =