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## Elementary Linear Algebra ??????

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### Elementary Linear Algebra R. Larsen et al. (6 Edition ... – PowerPoint PPT presentation

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Title: Elementary Linear Algebra ??????

1
????
• ???????????
• ??????? ??

Elementary Linear Algebra

?????? R. Larsen et al. (6 Edition)

???
?????
2
??
• ??? ???????
• ??? ??
• ??? ???
• ??? ????
• ??? ????
• ??? ????
• ??? ????????

3
??? ???????
• 1.1 ?????????
• 1.2 ????????-?????

Elementary Linear Algebra

?????? R.
Larsen et al. (6 Edition)

????????
4
1.1 ?????????
• n????????? (linear equation)

• ??
• (1) ???????????????????,?
• ?????????????????????

(2) ??????????????? ?
???? 1.1? pp.2-3
5
• ?? 1??????

???? 1.1? p.3
6
• n?????????? (solution)
• ??? (solution set)
• ??????????????????

???? 1.1? p.3
7
• ?? 2????????? (parametric representation)

???? 1.1? pp.3-4
8
• n???m???????? (system of linear equations)
• ??? (consistent)
• ????????????
• ???? (inconsistent)
• ?????????

???? 1.1? p.5
9
• ???????????,??????

(1) ???????(?????) (2) ????????(?????) (3)
?????(??????)
???? 1.1? p.6
10
• ?? 4(?????????)
• (1)
• (2)
• (3)

???? 1.1? p.6
11
• ?? 5?????(back substitution)????????????

???? 1.1? p.7
12
• ?? 6?????????????????

???? 1.1? p.8
13
• ?? (equivalent)
• ?????????????????,
• ???? ??????????
• ???????????????????

(1) ??????
(2) ???????????
(3) ??????????????
???? 1.1? p.8
14
• ?? 7???????????????????????

???? 1.1? p.9
15
???? 1.1? p.9
16
• ?? 8?????????(????(??)??)

???? 1.1? p.11
17
• ????????????

???? 1.1? p.11
18
• ?? 9?????????(?????)

???? 1.1? p.12
19
???????????
???? 1.1? p.12
20
????? (1.1?????)
• linear equation ?????
• system of linear equation ??????
• solution ?
• solution set ???
• parametric representation ?????
• consistent ???(??)
• inconsistent ????(?????)
• equivalent ??

21
1.2 ????????-?????
• m?n ?? (matrix)
• ??

(1)?????????(entry)aij????
(2)?m?n???????(size)?m?n
(4)??????,??a11, a22, , ann?????? (main
diagonal)???
???? 1.2? p.18
22
• ?? 1 ?? ??
• ??
• ????????????????????

???? 1.2? pp.18-19
23
• m????n???????????

???? 1.2? p.19
24
• ???? (augmented matrix)
• ???? (coefficient matrix)

???? 1.2? p.19
25
• ??????? (elementary row operation)
• ??? (row equivalent)

?????????????????????,???????????
???? 1.2? pp.19-20
26
• ?? 2(?????)

???? 1.2? p.20
27
• ?? 3????????????

????
???????
?????
???? 1.2? p.21-22
28
• ?? 3????????????

????
???????
?????
???? 1.2? p.22
29
• ????? (row-echelon form)

(1)????????????
(3)??????????,??????1???? ?????1???
• ?????? (reduced row-echelon form)

(1) (3) ?? (4)???1????????1?????????
???? 1.2? p.22
30
• ?? 4???????????????????

???? 1.2? p.23
31
• ????? (Gaussian elimination)
• ??????????????
• ??-????? (Gauss-Jordan elimination)
• ???????????????
• ??

(1) ??????????????
(2) ???????????????(?????? ???????????)
???? 1.2? p.27
32
• ????????????????????

???? 1.2? ??
33
?????
?????
?????
??????
???? 1.2? ??
34
• ?? 7???-??????????????(???)

?
???? 1.2? p.27-28
35
• ?? 8?????????(?????)

???? 1.2? pp.30-31
36
???????????
???? 1.2? pp.30-31
37
• ?????????? (homogeneous system)

????????????????, ?????????
???? 1.2? p.30
38
• ??? (trivial solution)

(??n????????)
• ???? (nontrivial solution)
• ?????????
• ??

(1) ????????????(consistent)??
(2) ???????????,???????
(3) ??????????,??????
(a) ?????????
(b) ???????????????
???? 1.2? p.30
39
• ?? 9??????????????

???? 1.2? p.30
40
????? (1.2?????)
• matrix ??
• row ?
• column ?
• entry ??
• size ??
• square matrix ??
• order ?
• main diagonal ????
• augmented matrix ????
• coefficient matrix ????

41
• elementary row operation ?????
• row equivalent ???
• row-echelon form ?????
• reduced row-echelon form ??????