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????

- ???????????
- ??????? ??

Elementary Linear Algebra

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

???

?????

??

- ??? ???????
- ??? ??
- ??? ???
- ??? ????
- ??? ????
- ??? ????
- ??? ????????

??? ???????

- 1.1 ?????????
- 1.2 ????????-?????

Elementary Linear Algebra

?????? R.

Larsen et al. (6 Edition)

????????

1.1 ?????????

- n????????? (linear equation)

??a1,a2,a3,,an????,?????b?????a1??????(leading

coefficient),x1??????(leading variable)?

- ??
- (1) ???????????????????,?
- ?????????????????????

(2) ??????????????? ?

???? 1.1? pp.2-3

- ?? 1??????

???? 1.1? p.3

- n?????????? (solution)

- ??? (solution set)
- ??????????????????

???? 1.1? p.3

- ?? 2????????? (parametric representation)

???? 1.1? pp.3-4

- n???m???????? (system of linear equations)

- ??? (consistent)
- ????????????

- ???? (inconsistent)
- ?????????

???? 1.1? p.5

- ???????????,??????

(1) ???????(?????) (2) ????????(?????) (3)

?????(??????)

???? 1.1? p.6

- ?? 4(?????????)
- (1)
- (2)
- (3)

???? 1.1? p.6

- ?? 5?????(back substitution)????????????

???? 1.1? p.7

- ?? 6?????????????????

???? 1.1? p.8

- ?? (equivalent)
- ?????????????????,
- ???? ??????????

- ???????????????????

(1) ??????

(2) ???????????

(3) ??????????????

???? 1.1? p.8

- ?? 7???????????????????????

???? 1.1? p.9

???? 1.1? p.9

- ?? 8?????????(????(??)??)

???? 1.1? p.11

- ????????????

???? 1.1? p.11

- ?? 9?????????(?????)

???? 1.1? p.12

???????????

???? 1.1? p.12

????? (1.1?????)

- linear equation ?????
- system of linear equation ??????
- leading coefficient ????
- leading variable ????
- solution ?
- solution set ???
- parametric representation ?????
- consistent ???(??)
- inconsistent ????(?????)
- equivalent ??

1.2 ????????-?????

- m?n ?? (matrix)

- ??

(1)?????????(entry)aij????

(2)?m?n???????(size)?m?n

(4)??????,??a11, a22, , ann?????? (main

diagonal)???

???? 1.2? p.18

- ?? 1 ?? ??

- ??
- ????????????????????

???? 1.2? pp.18-19

- m????n???????????

???? 1.2? p.19

- ???? (augmented matrix)
- ???? (coefficient matrix)

???? 1.2? p.19

- ??????? (elementary row operation)

- ??? (row equivalent)

?????????????????????,???????????

???? 1.2? pp.19-20

- ?? 2(?????)

???? 1.2? p.20

- ?? 3????????????

????

???????

?????

???? 1.2? p.21-22

- ?? 3????????????

????

???????

?????

???? 1.2? p.22

- ????? (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

- ?? 4???????????????????

???? 1.2? p.23

- ????? (Gaussian elimination)
- ??????????????

- ??-????? (Gauss-Jordan elimination)
- ???????????????

- ??

(1) ??????????????

(2) ???????????????(?????? ???????????)

???? 1.2? p.27

- ????????????????????

???? 1.2? ??

?????

?????

?????

??????

???? 1.2? ??

- ?? 7???-??????????????(???)

?

???? 1.2? p.27-28

- ?? 8?????????(?????)

???? 1.2? pp.30-31

???????????

???? 1.2? pp.30-31

- ?????????? (homogeneous system)

????????????????, ?????????

???? 1.2? p.30

- ??? (trivial solution)

(??n????????)

- ???? (nontrivial solution)
- ?????????

- ??

(1) ????????????(consistent)??

(2) ???????????,???????

(3) ??????????,??????

(a) ?????????

(b) ???????????????

???? 1.2? p.30

- ?? 9??????????????

???? 1.2? p.30

????? (1.2?????)

- matrix ??
- row ?
- column ?
- entry ??
- size ??
- square matrix ??
- order ?
- main diagonal ????
- augmented matrix ????
- coefficient matrix ????

- 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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