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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)

??a1,a2,a3,,an????,?????b?????a1??????(leading
coefficient),x1??????(leading variable)?
  • ??
  • (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 ??????
  • leading coefficient ????
  • leading variable ????
  • 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)????????????
(2)??????,?????????1,????1 (leading 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 ??????
  • leading 1 ??1
  • Gaussian elimination ?????
  • Gauss-Jordan elimination ??-?????
  • free variable ????
  • homogeneous system ????
  • trivial solution ???
  • nontrivial solution ????
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