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▶Linear Algebra and its Applications 3rd 3판 솔루션

등록일 : 2011-07-10
갱신일 : 2011-07-10


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Linear Algebra and its Applications 3rd D. Lay - Addison Wesley


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 obt…(생략)
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