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CABL ?5@2K9 MB0? 0;3>@8B<0 ?@O<>3> E>40 <5B>40 0CAA0 ?@82>48B A8AB5<C : 284C: x -  3*y +    z = -6 0 +    0 -  2*z =  2 0 + 11*y - 20*z = 42. @8 MB>< 2A?><>30B5;L=K9 <0AA82 8=45:A>2 A>45@68B =0G0;L=K5 7=0G5=8O Index[1] = 1 Index[2] = 2 Index[3] = 3. =0G5=85 3;02=>3> M;5<5=B0 A[2,2] @02=> =C;N. ;3>@8B< ?>8A:0 3;02=>3> M;5<5=B0 2> 2B>@>9 AB@>:5 =0945B =5=C;52>9 M;5<5=B 2 B@5BL5< AB>;1F5 (K=3). 5=O5< ?5@5<5==K5 y 8 z <5AB0<8, B.5. >ACI5AB2;O5< ?5@eAB0=>2:C 2B>@>3> 8 B@5BL53> AB>;1F>2 <0B@8FK . >A;5 G53> ?>;CG05< x +    z -  3*y = -6 0 -  2*z +    0 =  2 0 - 20*z + 11*y = 42. @8 MB>< 2A?><>30B5;L=K9 <0AA82 8=45:A>2 ?>;CG8B =>2K5 7=0G5=8O: Index[1] = 1 Index[2] = 3 Index[3] = 2. 0;L=59H85 2KG8A;5=8O ?@>872>4OBAO ?> ?@82545==>9 2KH5 AE5<5 <5B>40 0CAA0 8 ?>A;5 >1@0B=>3> E>40 1C45B ?>;CG5=> @5H5=85 8AE>4=>9 A8AB5<K x = 1;  y = 2;  z = -1. >=5F ?@8<5@0. 3.3.3. ;3>@8B< ?>8A:0 3;02=>3> M;5<5=B0 A 8=45:A0F859 =><5@0 AB>;1F0 M;5<5=B0 <0B@8FK @54K4CI89 20@80=B 0;3>@8B<0 =5 8<55B >3@0=8G5=89 8 <>65B 8A?>;L7>20BLAO 4;O ?@>872>;L=>9 A8AB5<K C@02=5=89. <5AB5 A MB8< <>6=> 70<5B8BL, GB> ?5@5AB0=>2:0 AB>;1F>2 <0B@8FK ?@82>48B : 4>?>;=8B5;L=K< 2KG8A;8B5;L=K< 70B@0B0< ?@8 2K?>;=5=88 <5B>40 0CAA0 (2 A;CG05 1>;LH>3> :>;8G5AB20 =58725AB=KE 2 A8AB5<5 ;8=59=KE C@02=5=89). ;O A=865=8O B@C4>5<:>AB8 2KG8A;5=89 2 A8;C B>3>, GB> =0A 8=B5@5AC5B ?>@O4>: 8A?>;L7>20=8O AB>;1F>2, 0 =5 8E <5AB> 2 <0B@8F5, F5;5A>>1@07=> 2 :0G5AB25 8=45:A0, >?@545;ONI53> 4;O M;5<5=B0 <0B@8FK  =><5@ AB>;1F0 <0B@8FK, 8A?>;L7>20BL 7=0G5=85 >4=><5@=>3> <0AA820 Index (A<. ?. 3.3.2.). ">340 ?5@5AB0=>2:C AB>;1F>2 <0B@8FK <>6=> 70<5=8BL ?5@5AB0=>2:>9 42CE M;5<5=B>2 MB>3> <0AA820 (A>:@0B82, B5< A0<K<, 7=0G8B5;L=> 2@5<O 2KG8A;5=89). @8 MB>< 4;O 4>ABC?0 : M;5<5=B0< <0B@8FK  2 :0G5AB25 =><5@0 AB>;1F0 A;54C5B 8A?>;L7>20BL 7=0G5=8O, E@0=OI85AO 2 M;5<5=B0E <0AA820 Index. ">340, GB>1K ?>;CG8BL 7=0G5=85 M;5<5=B0 <0B@8FK  4;O I->3> C@02=5=8O 8 J->9 ?5@5<5==>9, =5>1E>48<> >1@0B8BLAO : M;5<5=BC <0AA820 A[I, Index[J]], 0 3;02=K9 M;5<5=B 8A:;NG5=8O =0E>48BAO 2 M;5<5=B5 A[I, Index[I]] (A<. 8A 3.2).  EMBED Word.Picture.6  @8 @50;870F88 B0:>3> A?>A>10 ?>8A:0 3;02=>3> M;5<5=B0 @5:><5=4C5BAO >1@0B8BL 2=8<0=85 =0 2>?@>AK B>G=>AB8 2KG8A;5=89.  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F8:;5 ?> ?5@5<5==>9 I >B 1 4> N 45;05< Index[I]:=I. ;O ?@8<5=8<>AB8 @0AA<>B@5==>9 AE5<K ?>8A:0 3;02=>3> M;5<5=B0 2> 2A5E >AB0;L=KE H030E 0;3>@8B<0 =5>1E>48<> 70<5=8BL 8=45:AK <0B@8FK  ?> A;54CNI5<C ?@028;C: A[I, J]  =0  A[I, Index[J]]. >A;5 >:>=G0=8O @01>BK <5B>40 0CAA0 ?@8 B0:>9 AE5<5 ?>8A:0 3;02=>3> M;5<5=B0 7=0G5=85 =58725AB=>9 x A =><5@>< i 2 8AE>4=>9 A8AB5<5 C@02=5=89 =0E>48BAO 2 M;5<5=B5 25:B>@0 x c 8=45:A>< Index[I] (B.5. 2 x[Index[I]]). 3.3.4. ;3>@8B< ?>8A:0 3;02=>3> M;5<5=B0 A  8=45:A0F859 AB@>: 8 AB>;1F>2 <0B@8FK +) @54K4CI89 20@80=B 0;3>@8B<0 ?>8A:0 3;02=>3> M;5<5=B0 ?@54?>;030; 8=45:A0F8N B>;L:> =><5@0 AB>;1F0 8AE>4=>9 <0B@8FK 8 >ACI5AB2;O;AO ?>8A: <0:A8<0;L=>3> ?> <>4C;N M;5<5=B0 2 7040==>9 AB@>:5. =0;>38G=>, <>6=> >ACI5AB2;OBL ?>8A: <0:A8<0;L=>3> ?> <>4C;N M;5<5=B0 2> 2A59 ?>4<0B@8F5 <0B@8FK , 0 =5 B>;L:> 2 AB@>:5. >=OB=>, GB> ?@8 MB>< 7=0G5=85 <>4C;O 3;02=>3> M;5<5=B0 2> 2A59 ?>4<0B@8F5 1>;LH5 8;8 @02=> 7=0G5=8N <>4C;O ;N1>3> M;5<5=B0 2 B5:CI59 AB@>:5. 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