










 !""#$
%&'()*+,-%./
01%23
( )
11 1 1
1
1
j n
i iij n
ij
m n
m mj mn
a a a
a a
A a
a a a
a
×
 
 ÷


= ⇔

= ∀


CD+E
1 2 1
3 4
b
c d
   
=
 ÷  ÷
−
   
FGH"#$I@JK
  LM N1   1 ? 
O567P&8Q
  M R/  S - & '(
1T-*
+,-%-./01?5
11
22
12 1
21 2
1 2
n
n
n n nn

a a
A
a
 
 ÷
 ÷
=
 ÷
 ÷
 
K
K
K
K
 VM N1 1 ./
56 7 L 8 < U V
DP&8Q
/O<
FGH"#$I@JK
MN1V1./
5678<UVDP
&8
1 0 0
0 1 0
0 0 1
n
I
 
 ÷
 ÷

3
-L∈ R.
L"SaL
/4
b3
\ef
/[ "`@S@`" XD/OZ
//[ X"`@Z`S"`X@`ZXDL=g5Z
///["`QS" XQg/:01Q
h
Z
/["`X−"ZSQ
[ XL"ZSXLZ"
/[X"`@ZS"`@
//[X`LZ"S"`L"
///[["S"
CY/./"-@-∈ M
h
-L- ∈
#-*
W]Wc"J"#$
/"Sa
/4
b
h5-
@Sa&
/4
b
5h
[

W]Wc"J"#$
CD+EM
( )
3
a) 1 4
2
 
 ÷
 
( )
3
b) 1 4
2
 
 ÷
 
1 2
1 2 3
) 3 2
4 5 6
1 4
c
 
 
 ÷
 ÷
 ÷
 
 ÷
 

h
4 1
A 3 0
2 7
−
 
 ÷
=
 ÷
 ÷
 
T
4 3 2
1 0 7
A
−
 
=
 ÷
 
( )
T
T
( ) A =Ai
( ) ( )
T
T T
A+B =A +Bii
( ) ( )
T

 ÷
−
 ÷
 ÷
=
 ÷
 ÷
 ÷
 
0 2 7
0 3 4
0 0 5
C
 
 ÷
=
 ÷
 ÷
 
2 3 5
0 0 0
0 1 3
D
 
 ÷
=
 ÷
 ÷
 
\W]W@G#_>x

b) B
3 0 3 0
4 1 6 7
 
 ÷
−
 ÷
=
 ÷
 ÷
− −
 
‚ƒ""#$CB„
11 1 1
1 2
ij
1
A
j n
i i ij in
n nj nn
a a a
a a a a
a a a
 
 ÷
 ÷
 ÷
=
 ÷

n
n n
a A a AA a A
+ + +
= − + − + + −
( )
1
1 1
1
1 det
n
j
j j
j
a A
+
=
= −
∑
‚ƒ""#$CB„
hV
11 12
21 22
a a
A
a a
 
=
 ÷
 

D?5ˆ&8q;oG'
uj;+•"‰
ˆhŠ
…"
ˆhˆ
&8O
&p'<1"%1%{
×
 
 ÷
=
 ÷
 ÷
 
1 2 3
3 3 1 2 3
1 2 3
a a a
A b b b
c c c
×
 
 ÷
=
 ÷
 ÷
 
1 2 3 1 2
/
3 5

‚ƒ""#$CB„
Nl
  D      
gT&1;9Ei01
DL//:y+,[
Lp/L/
L//:y1‹%&?L}
CD+E
0lM"SX
/4
Z
h
[R/*
( )
0
0 0
1
det ( 1) det 1
n
i j
i j i j
j
A a A
+
=
= −
∑
( )
0
0 0

 
 ÷
−
 ÷
=
 ÷
 ÷
 
‚ƒ""#$CB„
D?M
X/Z R/ ?  O 56 7  % +, X%
%Z*+p/'(T
*:5jD1p/[
X//Z R/ j O 56 7  % +, X%
%ZY/•%'(L-TgY/
&8ŒjY/L
(i) (j)
A B→
:
(i):= (i) + k (j)
A B→
‚ƒ""#$CB„
X///Z/O&8DO567
%UVD[
X/Z      * / +, &? L} • 0v Y/
T&8Q[
XZ+y"S+yX"

Z-∀"∈


"#$ Ž^
iM"01?5[=n
/@•?5'"3@S@3"SJ


Tk*/"01L1@01
"[
klM"X=*Z01+;?
CD+EM/
1 3 7
A 2 1 2
7 1 4
 
 ÷
=
 ÷
 ÷
−
 
2 5 1
B 22 53 12
9 22 5
−
 
 ÷
= − −
 ÷
 ÷
−
 

 
D"[@1@["
"#$ Ž^
ef
"

LL/1•L/+y"rQ
( )
i+j
ij ij n
b = -1 detA M∈
T
11 12 1n
21 22 2n
-1 T
n1 n2 nn
b b b
b b b
1 1
A B
detA detA
b b b
 
 ÷
 ÷
⇒ = =
 ÷
 ÷
 
K

T56,0/01"

"
N lM R/ &/= p/- = *  +, &8 Q 9 %
 / & T +… 0/ 1 L= 0M  "
LL
CD+EMT'
2 1 2
a) A 1 2 1
1 2 3
 
 ÷
= − −
 ÷
 ÷
 
1 3 4
b) A 1 5 1
3 13 6
−
 
 ÷
= −
 ÷
 ÷
−
 