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
Giải toán trên
6.1. ĐẠI SỐ MA TRẬN

Transpose Matrix


!"#$% !"&
'(#$%&$)*+'(&
!,(-./,$0"&
1%(#$%)*+,+$'234-)5
!*&*+ 
'6"78
/01&$Inverse Matrix&
2

!,(-,9)$0//&
1%(34567,$)*'$8/: ;'))(2!39
$<!(3$+*+234-)5
=>?
!%@9,$:;&)"2
(" 2
Lưu ýA"(" 
5,)B0
  $0 //&  C  @3
 #  5  DE =
4=F
G=
2H//,
)  4     
G=


  
-8!"#@3
F
G=
$IDEI
4&  J  9K  L  #  9K
;L@3$9M.
  8  !  "#
///<&2'7-97+=/<9<N'(,$>(+2
'6"78

5?multiply&$@AA

!,(-$0/B&
1%( 33C $)* '$8 /:   ;'))(2! 39
$<!(33C234-)5
=OP
!%@9,$ !"&)" Q!%@
9,$= D&)"/
(" 2
Lưu ýA"(" 5,)B0$0/B&C@3#5DE
=4=F2H//,)4-8!"#@3
F$IDEI4R3-I@IS3-T@I&J9KL#9K;L@32
'7-97+=/<9<N'(,$>(+2
'6"78
<E0F$Matrix determinant&G!+

!,9,U$0=H&
1%(3!73$)*'$8/: ;'))(2!39
$<!(3!73234-)5

!%@9,$:;&)"2
(" 2
=O=
6.2. GIẢI HỆ PHƯƠNG TRÌNH TUYẾN TÍNH
1%(,&'+)3+&&'*FV@W(2X7)N:-)3+&&'*
6(.)
1%(&&'*I##24*Y
34-)5DDGZ
• '$8![,&'+##2$2
• '$8\ 2
')]W'))(^@3(A)(W2
6E#J_-`R.7







=+−
−=++
=++
=++
=TIIa
b>
>I
aa
zyx
zyx
zyx

zyx
 KL@L@$&MNL1EO+'
=Oa
=V=bb(DE;9c2
a>(#F@Qa>(#F.a>(#Fd2
e=P(;f#2
e=P(,9KFf#2A"@)%.(F
-`R`Uf#2
4M$9/#2
41$$VaV>&(,7-F-`R2
L MLP$1$L@$&M
Bước 1
HD3"#4M$$!/!"2
1%(M33C/"Q:;$)*'$8/:
;'))(2!39$<!(33C+=/<3g:--
'(,$>(+2
Bước 2
("4)0!/2
_!,&'+LW&&'*X-#)hg,&'+++*

=OI
Set Target Cell1)\9/09,,5!/;^/,R!R/2X79\-
+@9,C.9#.2
Equal To("49D36'+&>+)";5,(/$R\
-))7;i7;-&2
Subject to the ConstraintsHM.(`@9,9c"49/)j
);$9c"()4,4i,4-&2("\##
@34-)5##&*$*-)#
(" 9/(54-,&'+)++*2
A"9)#F4-)5,&'+'$8)\!,&'+2

X7"78#V@W(0)(kfound a solutionl
mj.!.++,&'+,&'$&9/("78;$7!7+*&+-$$'
6'+*^n"78A)(WLR9:(5,"94F7&2
=OT
o78;
XR;3.,)4M$i9\,)4
1$248S$0T9j.9gp,Upf#2q.F
-`R(@r=Q.rGadra2
6.3. QUI HOẠCH TUYẾN TÍNH
)5.7()R/$.95&F4.7s$@&
;-:-1⊂t

9:@9,4-`Ru)*3-`R
.7)2
A@$&MUDVWM
'R7#@
=
@
a
222@

))
s$@&r

=
n
j
jj
xc
=

→$.@& $O2=&
Bj9c"


=
n
j
jij
xa
=
≤

r=222
=
 $O2a&


=
n
j
jij
xa
=
≥

r
=
v=222
=
v

a
 $O2I&


=
n
j
jij
xa
=
r

r
=
v
a
v=222 $O2T&
@
w
≥Pwr=222
=
@
w
≤Pwr
=
v=222
=
v
a
≤2 $O2>&

'));
s!(hm mc tiêupU$O2a&G$O2>&!(4rng buc2
H/@r$@
=
@
a
222@

&∈t

Bj!4!(4phương !n2
'-:-3-`!(mi"n rng buc2
]4-`)j$O2=&!(phương !n t#i ưu.4l$i gi%iF)
9j)2
=O>
/X$1$L@$&MUDLYO+'
1%(,&'+)3+&&'*FV@W(2
AZ4-[5\).]D-^D,_5C`
]4@-D9,@3()5-f(A
=
A
a
2H/(9:49`,
A
=
KT9`,(q
=
>9`,(q
a
2H/(9:=9`,A

a
KI9`,q
=
a
9`,q
a
2_49`,A
=
(>P
9<49`,A
a
(IP9<2
mB@-;@3);
9`,-fA
=
A
a
9/g-(
(37i@-C6=aPP
9`,(q
=
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q
a
2
3GK&Ma
_!@
=
@
a

(K(:(#9`,-fA
=
A
a
K@32A#9`,(q
=
K
6(T@
=
vI@
a
21)@-C6=aPP9`,(q
=
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a
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a
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=
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a
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=
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a
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=
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=
vIP@
a
→@

9c"
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=
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a
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>@
=
va@
a
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@
=
≥P@
a
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X$1$ML1E
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))2.-/+7#9K)57
4F7#962
APM.D0R@3;-)4--9K3"x
=OO
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=P)0a1a2o78
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  --    @3  .  95
ePP    $tuy nhiên vẫn
chưa sử dng hết vật liệu

trong kho&2
AP/'#)2
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,&'+++*
Tóm tắt tham s# yêu cầu của Solver
=Ob
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= AW'WW(( m[; ?
a V8(') ]@]q(W)s
$()5)&
]@
I .W(( 7 a1a
T AwW)W) 4 VOVbOb
A"9)#F4-)5A)(W'$8)\!,&'+9/V@W(J
9K)2
.dW1K0eSK*
LAZ4-[5[fg5D.DhC)Di5Djk5
]4@-y0K()5Uyg:-'
=
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a
)\C(
77="'
=
UI9`,DDz1
=
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a
$m.9
)&=9`,DDz1

I
${)W&Q="'
a
U=9`,1
=
=9`,1
a
a9`
,1
I
2]p|y)\K#/OP9`,1
=
TP9`,1
a
OP9`,1
I
2
mB  @  -  K  
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=
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a
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y))L9)#D
Dz)| yF \
L9/g#cU
y(B32)7="'
=
aP9<="'
a

=>
9<2
3GK&Ma
=Oe
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=
@
a
(K(:(#"Uy'
=
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a
K)p|y2A#9`,31
=
6)p|y(I@
=
v@
a
R7@
=
@
a
KBj
I@
=
v@
a
≥OP
'`9/9-UKc31
a

1
I
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=
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@
=
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a
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@
=
va@
a
≥OP
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@
=
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a
≥P2
A#cUy$K(/&israP@
=
v=>@
a
$9<&2
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=

@
a
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sraP@
=
v=>@
a
→
9c"
I@
=
v@
a
≥OP
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=
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a
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@
=
va@
a
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@
=
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a
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LX$1$ML1E

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'-)4--9K$'='a&r$aPaP&2o78)3.g#c
UyF--.95bPP2
AP/'#)2
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hg,&'+++*
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q39c9*F@(R•J7"3~

=bT

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