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Regla de Cramer - MATRIZ 3X3

x+y+z = 1

x-2y+3z =2

X +z =5

1=

|1 1 1

2 2 3

5 0 1|

|1 1 11 2 31 0 1

|=

[(20 )( 215 )+( 0+10 )](20 )( 13 )+( 0+2 )

=2

2

2=

|1 1 1

1 2 3

1 5 1|

|1 1 11 2 31 0 1

|=

[( 215 )( 13 )+( 52 )](20 )( 13 )+( 0+2 )

=8

2

3=

|1 1 1

1 2 2

1 0 5|

|1 1 11 2 31 0 1

|=

[(100 )( 52 )+( 0+2 )](20 )( 13 )+( 0+2 )

=11

2

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Regla de Cramer - MATRIZ 4X4

x+2y-z+3t = -8

2x +2z-t =13

-x+y+z-t =8

3x+3y-z+2t=-1

1=

|8 2 1 3

13 0 2 1

8 1 1 1

1 3 1 2|

| 1 2 1 3

2 0 2 1

1 1 1 1

3 3 1 2|=

64

28

2=

| 1 8 1 3

2 13 2 1

1 8 1 1

3 1 1 2|

|

1 2 1 3

2 0 2 1

1 1 1 1

3 3 1 2

|

=66

28

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Calcul! de cada "# "1# "2# "3# "4

"=Me$r%

m11= [0 2 11 1 1

3 1 2] = & '2+1( ) 2'2+3( ) 1'-1-3( = & ) 1& + 4 = )*

m12= [ 2 2 1

1 1 1

3 1 2] = 2'2-1( ) 2'-2+3( ) 1'1-3( = 2 ) 2 +2 = 2

m13=

[ 2 0 1

1 1 13 3 2]

= 2'2+3( ) &'-2+3( ) 1'-3-3( = 1&-&+* = 1*

m14= [ 2 0 2

1 1 1

3 3 1] = 2'-1-3( ) &'1-3( + 2'-3-3( = -8-&-12 = )2&

= -6-2+16+20=28

--------------------------------

"1=Me$r%

m11= [0 2 1

1 1 1

3 1 2] = & '2+1( ) 2'2+3( ) 1'-1-3( = & ) 1& + 4 = )*

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m12= [13 2 1

8 1 1

1 1 2] = 13'2-1( ) 2'1*+1( ) 1'-8-1( = 13 ) 34 + = -12

m13= [13 0 18 1 1

1 3 2] = 13'2+3( ) &'1*-1( ) 1'1*+1( = *5-&-1, = 48

m14= [13 0 2

8 1 1

3 3 1] = 13'-1-3( ) &'-8-3( + 2'24-3( =-52-&+42 = )1&

2 = -6+12+48+10=64

--------------------------------

2=Menor:

m11= [13 2 1

8 1 1

1 1 2] = 13 '2-1( ) 2'1*-1( ) 1'-8+1( = 13 ) 3& + , = )1&

m12= [ 2 2 1

1 1 1

3 1 2] = 2'2-1( ) 2'-2+3( ) 1'1-3( = -2 -2 +2 = -2

m13=

[ 2 13 1

1 8 1

3 1 2]= 2'1*-1( ) 13'-2+3( ) 1'1-24( = 3&-13+23 = 4&

m14= [ 2 13 2

1 8 1

3 1 1] = 2'-8+1( ) 13'1-3( + 2'1-24( =-14+2*-4* = )34

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2 = -10+2+40+34=66

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