2.1 3K
eo HRNEN
FRAT m xn PRE m FF OIE
mt Gn2 “dns
MY fi — (PSE RE (matrix), FILLE Ac
TE EREP , BEA Bm AAT (row), BARA HCO A (column), SEPEP AY
8 — (EAB HUH ETE HR (clement). RTA a, ARMM M TERT, Fey
i, j RRM ULF AOD FHT. HM, an RARER BOAT
Ro MATER AT AA (ag) RA. ARTA (ag) mn RIGA m Fn
Fl, AA, RMGKEH mx n ER, mx n ASE RERTHY (order). fan,
( 54 8
6 3 10
) Bt 2x3 sere.
24 m =n BY, SE PREM fe m BEIT RE (square matrix of order n). 40,
21 6
0 0 5 | —T=BFRES
sl 4 =3
m= 1 APH ERY 1x n SERE (ay a ain) MH AATSERE (row matrix), an
n= LASHER AY m x 1 EE 8 ZUSERE (column matrix). £0,
an
nn
2
(-1 0 3 ~4) Jefrsare, 3 | EPI.
1
eo HSE
RDA ERE A 5 BME m xn EME, AIC R TCR BS, BBA 5 Bo
WCHESERE (equal matrices), iZfF A=B.
arem(S tT ).(3t? 8) kate cet
ate -1
ASI XL, PT 2 MTP RETO RTS, LL
a=5+b
atb=c
dzat+e
c=-1
MTA BM, Ma=2, b= -3, c=-1, d=1
oe Fae
TER HEE 6 HE FO ACRE AE RE (zero matrix), 12fF Oo PARE AT VATE ERB,
HER, CREM. we,
00
00
00
(3 0) wax asesine (
) 2b
32 .
1 ea=( 4 o) RA
, 23 8 12 ee
2 ita=(¢ fo). B=( ap) RHA AGE By
2-3 0 -2 30
3 Ba=(5 boo) Bel 3 oy le #
(a) A+B (b) 2A-B
costa - sina si sine
tenn ete en wel
(a) A+B (b) 3(A+B)
5. Rw, x, y, 2 oth
—15— 2.4 RAR
@ ERR
BAH —* 1x p BATE (aun an ay), BHF px 1 BASE
» BUTE LATER A STEPE BAYER AB A
bu
b
AB= (an az“ ay)|
bps
= (anbutanbat + aipbp)
BRB A 1x1 PERE
GS ith:
2
(@ @ -2( 4) () G -4 | 3]
4
(3x14 (-2) x4)
m @) @ -2( 4)
(=5)
weil
(b) (3-4 7 od |: (3x 2+ (-4)(-3)+1x4)
= (22)
BA H—T mx pH, BAT px 1 AR, BAAS BNR
au a2 ay bu
ba
ay
Gn dm2 “* Onp auibis + aiaba + ayy bps
aubu + ambut
midi + Amzb2 +
RARBA m x 1 SEP.
ae fs} S29
3
2-1 0 2x34 (-1)x (-5)+0x9
wow (l i -2] (ebaaxtesveans
ll
~ oa!
w (SC) -(223)
BEATE mx p EME, Bp xn Ki, BAAS BAIR AB=CH mx n
FE, EAVICR cy WERE AR i THT SEM BAIR j WM ICR ORAZ A,
ay an ay ay bu bi by bie
an an an" ay bu baz by “baw
bn bs by
ay a2 as ay
co by
eu en ey mt ein
en en ey em
FOP cy = aub yy + aabr +7 + aybyy
—1— ht)
a7
PTET, — RR TG — RT, MUR A
HR.
Anxy SByan WOH, AAA p WBA pt, RRACH—*
mxn Brisa. BD
mE (20k
(2° ( 143
41 -201
@{ Ateonee 2x4+0x0 2x340x1)
4x1¢1x(-2) 4x441x0 4x341x1
«{? 8 6
“\ 2 16 13
123 :
emmra=( 5 1) B=] 0 ABS BARSARL? WR
=
A, RHEIN.
seme (} 7} ) eaxssere, sopem = 3x SERRA NR
=i
GF BT, UL ABA X.
1
123
we (Sf
lx 1+2x0+3x (-1)
Ox1+1xO04+1x (-1)
=({-?
-1
BI WMARSF A MTR, MLA BA RHEL. Pl SHURA] ABAR XM, BAR-TABX. WRBALABX, ABS BA
SE — EAB?
BIO CAP PI A, B, ABS BA:
1-1 11
a} ® (2)
-1
(b) A= (1 1 0. 8-| ‘|
(a) a =(
| 14 2 2
(a) aB=(_ | heey adel 3)
11 1 <1 00
= i wt lloy Ce i
=1)
(b) AB= (1 1 0)} 0 | =(-1)
3
=1 =1 =1 0
Bpa=| 0 | 10 =| 0 0 0
3 393 0
Hb HAS BF BT a = AB # BA
a | “! 3
B10 CRIA = 1 61) +Be 2 ai C=
aR (AB)C 5 A(BC). WAH AHS?
-1 3
m case-(7 ~> 1) ee % 1
2 8 1 “i 8
a [ is
-(7™ 32
-29 9
AY LAE (ABYC = A(BC) .
RE:
(1) PEFR, BO (AB)C = A(BC)
(2) REET TH LR RT MN A,B
A(B+C) = AB+AC
(B+C)A = BA+CA
(3) Bik WMH, MW R(AB) = (KA)B = A(kB)
2 2c
+E (1~ 10):
1 1
waa af] 2 [a]oes
3 3
= (7 5)(5 9)
s
1
ya
1
os
'
wn
woo
2
1
on
mex
ae)
~
oun
1
eos
- on
YY
wn
2 9.
(rd) wT a), T)
2 3 1-21
- = rt
ema=(T 3). B= (5) 5 )). eam eorex? ea
EX, HH,
, 30 zs 14 =
-ata= (7 f) Bs 71) e8 (9 23).
(a) (AB)C=A(BC) (b) A(B+C) =AB+AC
, ei i _( 03 | a
. A= ( parle ®e( 93) c= (fo). ae
(a) (A+B)C=AC+BC (b) C(A+B)=CA+CB
. 00 HY oe.
a= (95) = oo) tHE
(a) AB (b) BA
13
‘ 132
as-| 2 i | a os): io
=1 3
(a) AB (b) BA
21 -22) | 751) ge.
ata ( 9 4). B= (75) c=( 3 3). ste:
(a) A(B+C) (b) B(2A +30)
+E
1 3 -2)f2 1 7 1 3-2 1-1 3
pcalia cs | o1 4 2-2 4
<1 4 ayhi @ -s -1 1 3)l-1 3 0
; sina cosa cose sina) a.
ee tee! B= (S22 SUE)
(a) AB (b) BA
=31— @ Shree
AL, Hie EBA Efi OY A A FOTO RAE 1, STOR AY
FERED
1 0 0
o 1 0
00 1
26 HABE SERE (identity matrix), iZfF 1. EAL HEM:
IA=A
AI=A
13 .
fin cmas( >) ). He
(a) A? (b) AY
@ (@ at=() ‘y(t 4) (b) A’ = APA
—_
70
=(4 7 = 714
=m = 7A
«{ 7 21
14 -7
WE) AP = ACA, A= ACATA
>) i 2d
HH:
20 20\*
nw (59) w (28)
2m (yi) w (1%)
(44) w() 4) 0Oaby 0Oaby
3. (a) | OO ¢ (b) | 0 0 €
000 000
4. iA = [ : RAP-A743A-41 6
a . { co89 - sind _{ cos@ sin 8 se ane
% ae ( or cos 8 Be (ee ey) + meaBe Ls
@ -1 .
6. #a=(5 1). em
(a) A?=5A-61 (b) A’=SA?-6A
dete, GKVA A AG AS
nites (4) ) sa bem. Ras bz ihisl
(a) #=0 (b) A (c) A?=A
2.5 RSE
sper a =| °* OO | ayer
sieeve | OP
Gin Gan 7 Onn
‘fi A 9478 SB RE (transpose matrix), icf A'H AT. Bian:
abe adg
WRA=| de f |, MAA =| 6 € h
ghia efi
1 5
1 3 2 Boe
map=(5 5 t).maw- [3-3
2 4
A, MH ARE mx n SE, ABZ AYE nx m SERFS fi 12 ka = ( a p= (77 3) oe:
-2 1!" 7 =
(a) (A+B)' (b) (A-B)’
(a) A+B = (b) A-B = ( = )
(a+B)' = ( és (a-By' = ( ; 3)
2.6 ieee
© HAR MEEE
BMA H—-TIRAM. MRE TORT B, 12419 AB, BA REF 1,
MART BAMA, RTRIE B OH Ahk A AYBAERE (inverse matrix), ic fe A’.
HY AA =F
ULE, a= (* S)oare(" *).
wm (SCE lor)
(rz Sig )elo 4)
au + bx =1
"= tr +dx =0
[= +by=l
cv +dy =0
Mik ABA, SAMY |Al=ad-be « Ot, WH
d
a
¢ b
= TAT © ©" “TAT 8" “TAT 7 = TAT
FDA oe EE A a AE, A
6
Al
d
we.) Tr oT
-TaT TAT
ye 1 ( d -b
=tat( ta)
piicmoree a = (° 5 ) siaeceensemaete |A| «0, seemierastie
Deer? 2) daliesoy
B13 PAS PRIA Re? RA, Ba ea
2 3) 304
wa=(Q 05 1s 20
() B= (
f= (a) |A| = 2x(-7)-(-3)x8
= 1040
. RT EE.
=7 @
a 3)
ose ot (
1
ula sly
wl= sie
(b) |B] = 0
SF PEAT SEP
fis eas (7 2), ROHN, Hs XA=L
Ld XA =1
XAA! = 1At
. Xa
1 5-3
=r | 3)
S _3
777
“| 4b 2
“7 7 >) 2e
593 2 4°03
1 A=] -1 0 4/,Be]-1 2 1 |, RA‘, BY
3°97 -5 0-4 5
tae(T op). ee
(a) 3a" (b) 3A)’
. 12 “2 -
3. tta=(5 5 )-8 (“) 3)-4
(a) (A+B)! (b) "+B" (e) (A-B)' (ad) a’—B"
4. FAAMFRARAMBH? PRA, SC wes
-2 -1 sing -—cosa@
cw ( 6 3) w ( cosa sina )
all ad 40
(7) 73) wag
; 31 -4 3 ;
s.tta=(55).B=("> 3).#
(a) At (b) Bt (ce) A'BT (d) (AB)~'
6. esotee( 1 >) waseee( 1). Re y Sth
2
-1 1 3 .
1 oa) Be (4g 3) + REREX. thal
(a) AX=B (b) BX=A
(c) A'X=B (d) AXA*'=B
8. #A=( 3 4) ) meeeRae, Rx it,
ab
9. a= (" |) Mesennae, Hie a= (arda,
ad @ SFr REA AE
SOR PEN PL, ERA A— TSP, ABARTH MEE
AB=BA=1=|0 1
FRSC A= TM BOM A ASABE, IPF A.
(—) URRRFRREBRE
(ar bo ey
x ae[ana]
ay bs ex
100
0
oo)
|
FEI A| PATIL TRAE, BAL, Bi, Ci, Aa, Ba, Ca, Ase Bay Cy HERP
Bi — 74
A, Bi G
re Bz e |
As By Cy
FEE Ae BEE, IEICE adj At
Ai Az As
wae Bp ® |
Cc
adj A PW ERE A HPEBESERE (adjoint matrix of A). IBA,
mye
ay by ev )f Ad
AvadjJA =| az b: e2 || Bi
as bs ow ILC
{Al 0 0
=| o lal oO
o o |al
= |All
= adjAvA
Ar
Bo
C:
eh Fy SR 5
As
Bs
Cs
—37- ERA ER
A(TApadia) = (Typ auia) A =
A" = Tyyaga (Al #0)
FLA = Br Ti BY SE PE FTE AY FOE RE JA] 2 0.
1-101
BIS RGA =| 2 1 3 | ABP A
304
1-1 1
La lAl =|2 1 3] = -10
3042
HELA | PARMAR RCE TU RIE,
|! 3] 2 3] 2) ‘|
re he
eal Bal -B cl }-(7# = =]
42 32 30 4
-4 -1 3
ial -kal bal
1 3] ~|2 3 201
-10 6 -4
as $ =1 <1
Sat 8
-10 6 -4
1 1
Ats-qp] 5 -1 “1
5-7 3
3 2
ley
i f. -t,
=| 7-2 10 10
a 2 _ pot
~2 10 710
—33— (=) DONT THR IEAERE
At A SEF AE
(1) afimEE REE
(2) HARE AMER
(3) eS — AOR — 45 ia A OY TER
3 AEH WE ON FT OTD PERE
FIRE RAMONES, Gt :
(a) JAR, + Ry RARER. =F Rs
(b) AAR: AAV > NF ATER
(co) A -2)R. + Rs RAH - 2A HMB = HMM L.
DLFEMESH EH (Causs elimination method) RB MEA AER ME = a Ee
CFF SPLIT ROPER TE A IE LD RR a
BK, MMS A.
“FT SHG 12 AYRE, SABLA Kn fag Ak — BB
Y-1 1
BMRA I) 2 1 3 |, FRAT —OTAKERE, IRIE PE AL,
304 2
p-141 100
Ail=|2 1 3 $010
3 94 21001
READ A, HSM MAAS AM TKO, PMR. KO
AO SRE Em AH SER (augmented matrix) < 2828 5G MERE ANS EP
(a) Sse ERE AT
(b) FAFA EHS A 1 EHR TY BS
(c) RA'=Bo
1-101
wave, wa | 3 1 3 |, Sei:
3.4 2
i-i # 100
All= 2 1 3 ol "|
304 2 oo1
2R+R(d -1 1 100
Pewee! og @ i a I °|
o 7-1 -301 ok 1-1 tf 1 0 0
Ree |O 1-3 $ -1-2 1
Oo 7-1 $ -3 0 1
~men (1 9-2 1 2-2 41
ReR | 0 1 -3 1-2 1
0 0 20 } -10 14 -6
10-2 $ 2 -2 )
-/O 1-3 } 1 -2 2
1 A ud a |
ae. 2 10 ~10
3 2
100 1=% 4
ae oro? -+ 4 4
7 “2 10 10
t A athe athe
oo “2 1 “10
2 2
1-3 $
at t+ to
Av =|! "2 10 10
A HL
~2 10 ~10
Sai 2f
VARS AF AF Fi 98 Bt 5k 48 BE (1-3) =
4-1 0 3140 1
ul si 2 4 2/2 5 1 3.)
2 01 121 2
VAR SH RF Fi 46 BE 0 GE $6 PE (4-6) =
11d 1 0 2
4.]3 2 -2 5.) 4 1 3 6.
2-1 3 2-1 0 al
1
3 2.7 FASE RR ETT
ASHE AT He WA SO PE ITA TCR 7G, STORE A, a Pe A
RRTAR IAL 20.
ais woanren {
a
3x - dy =6
Sx +2y =-3
DISSE RICA. Jr FEAL TT NRE
(372) )- (8)
es Jea(§
a (*)= a(§
nF a= dell 3g
(5) -a6( 5 3)(4)
= 36( 39)
IRSUTTA TERE SR ARR FAR SRC RAS HE OTL He AE WR 9,
RENERA EER.
‘ Lor+R) :
-44 Be 10} oO
(3 nq <3!) ~—— Ise | al
gia (oo
a= x a-y tz ad
4x -4y te =
x+y nz
BIT RETA BA |
Uw A. Dy RSH FE Be
ep
-|n ln io
A]O aa Aen
ot
aa wla sen
HR AT =
An alm oe
Ala aja alm
tot
Aa Mla ain
a
—42- PR WARGMTTA TCR AR HEAR NC HR RT He A WE,
RENEKMMSER,
1-1 1} 4 ee 1-1 1 4
4-4 1 basal e 0-3 -9
12-1 1 0 3-2 b <3
1-1 1} 4
wR fg 3 -2 | 3
0 0-3 } -9
1-1 t 4
' -1
: 3
= ,
talafiofe
|e
co
ou
1
2 BINS
Son aa
oro
-co
wee
Saat by as
x=2, y=l, 2=3
3) 2g
TAF 5 RA AB:
‘. (ena , [ine see2e
+y =38
x - by = 16
on ne «{
ety -ze|l
5. {x 2x -3y +2 =0 6. |
Qnty +2 =5 x +3y 432 =4
nity ted x -2y 25
[sya 8. foes “aes
x Qy tes x tdy-2 =0
9. (x t4rr42e5=4 10.
2x1 -2xrtay=4
x1 -2x243x3=3
—43— BRDB2
392 1
1 0-1/5
5 4 3)
1, Bde X+
4 Ses
nem { 2)ea 2] «(2 ] 403
3. ema * )e3( 2 )= (3 DY as
HH (4-8) =
eCpaey ecg)
. etea= (5 *).p=(3).aan= (9). kab
2
i we O) RAtBEAB, Ray by ee
ui, eeaa = (5 U4 3). (5 KA, Be
2 1
ie
(a) (A+B)’ (b) AB
3-2 -3 1) ,
13. CHA = 4-3 » B= ( D) rf a
(a) A” (b) BY (e) AB (a) (AB)
ACF FIsE RRA EE (14-15) :
1 0 3 1 2-3
14. 3 1 9 «| 2-1 -4
-2 2 -4 -2 5 1
a 16. RAEREX, &
@ (7 3)x-(12)
5 o1
(w) ( 5 3) x (4 : 4)
MAF | Rte ALS (7-20) =
x+2y 42225
r | 18. | 2a +6y 452
20.
19 |
x52 +10=0