Resolución de ejercicios de la práctica.docx
5
Resolución de ejercicios de la práctica (4 en total) Número 1 A= ( 1 1 −1 1 −1 1 1 1 1 ) A 1 = [ a 11 ]=1 A 1 −1 =¿¿]=1 Segundo paso A 2 = ( 1 1 1 −1 ) u 2 = 1 v 2 =1 a 22 =-1 ∝ 2 =-1-1.1.1=-2 P 1 =1+ 1.1.1.1 −2 = 1 2 q 2 = −1.1 −2 = 1 2 r 2 = −1.1 −2 = 1 2 A 2 −1 = ( 1 / 2 1/ 2 1 / 2 −1/ 2 ) Tercer paso A 3 = ( 1 1 −1 1 −1 1 1 1 1 ) u 3 = ( −1 1 ) v 3 =( 1 1 ) a 33 =1 ∝ 3 =1-( 1 1 ) ( 1 / 2 1 / 2 1 / 2 −1 / 2 )( −1 1 ) =2 P 2 = ( 1 / 2 1/ 2 1 / 2 −1/ 2 ) + ( 1/ 2 1 / 2 1/ 2 −1 / 2 )( −1 1 ) ( 1 1 ) ( 1 / 2 1/ 2 1 / 2 −1/ 2 ) 2 = ( 1 / 2 1/ 2 0 −1/ 2 ) q 3 = −( 1 1 ) ( 1 / 2 1 / 2 1 / 2 −1/ 2 ) 2 =(−1 / 2 0) r 3 = − ( 1 / 2 1 / 2 1 / 2 −1 / 2 )( −1 1 ) 2 = ( 0 −1 / 2 ) A 3 −1 = ( 1 / 2 1 / 2 0 0 −1 / 2 −1 / 2 −1 / 2 0 1 / 2 ) Número 2
-
Upload
carlosramirezruiz -
Category
Documents
-
view
219 -
download
1
Transcript of Resolución de ejercicios de la práctica.docx
Resolución de ejercicios de la práctica (4 en total)Número 1
A= (1 1 −11 −1 11 1 1 )
A1= [a11]=1
A1−1=¿¿]=1
Segundo paso
A2=(1 11 −1)
u2= 1
v2=1
a22=-1
∝2=-1-1.1.1=-2
P1=1+1.1.1 .1
−2 =12
q2=−1.1−2
=12
r2=−1.1−2 =
12
A2−1=(1/2 1/2
1/2 −1/2)Tercer paso
A3=(1 1 −11 −1 11 1 1 )
u3= (−11 )v3=(1 1 )
a33=1
∝3=1-(1 1 )(1/2 1/21/2 −1/2)(−11 )=2
P2=
(1/2 1/21/2 −1/2)+
(1/2 1/21/2 −1/2)(−11 )(1 1 )(1/2 1 /2
1/2 −1 /2)2
=(1/2 1/20 −1/2)
q3=−(1 1 )(1 /2 1/2
1 /2 −1/2)2
=(−1/2 0 )
r3=−(1 /2 1/21 /2 −1/2)(−11 )
2=( 0
−1 /2)
A3−1=( 1/2 1/2 0
0 −1/2 −1/2−1 /2 0 1/2 )
Número 2
A= (1 2 −12 −1 12 1 2 )
A1= [a11]=1
A1−1=¿¿]=1
Segundo paso
A2=(1 22 −1)
u2= 2
v2=2
a22=-1
∝2=-1-2.1.2=-5
P1=1+1.2.2 .1
−5 =15
q2=−2.1−5
=25
r2=−1.2−5 =
25
A2−1=(1/5 2/5
2 /5 −1/5)Tercer paso
A3=(1 2 −12 −1 12 1 2 )
u3= (−11 )v3=(2 1 )
a33=2
∝3=2-(2 1 )(1/5 2 /52/5 −1 /5)(−11 )=2,2
P2=
(1/5 2/52 /5 −1/2)+
(1/5 2 /52/5 −1 /2)(−11 ) (2 1 )(1 /5 2/5
2 /5 −1/2)2.2
=(0.2727 0.45450.1818 −0.3636)
q3=−(2 1 )(1 /5 2/5
2/5 −1/2)2.2
=
(−0.3636 −0 .2727 )
r3=−(1 /5 2/52 /5 −1/2)(−11 )
2 .2=(−0 .09090.2727 )
A3−1=( 0.2727 0.4545 −0.0909
0.1818 −0.3636 0.2727−0.3636 −0.2727 0.4545 )
Número 3
A= (2 3 13 −1 24 2 5)
A1= [a11]=2
A1−1=¿¿]=1/2
Segundo paso
A2=(2 33 −1)
u2= 3
v2=3
a22=-1
∝2=-1-3.(1/2).3=-11/2
P1=1/2+(1/2).3 .3 .(1/2)
−11 /2=111
q2=−3 .(1/2)
−5=311
r2=−3.(1/2)
−5=311
A2−1=(1 /11 3 /11
3 /11 −2 /11)
Tercer paso
A3=(2 3 13 −1 24 2 5)
u3= (12)v3=(4 2 )
a33=5
∝3=5-(4 2 )(1/11 3/113/11 −2/11)(12)=2,6364
P2=
(1 /11 3 /113 /11 −2 /11)+
(1/11 3 /113/11 −2/11)(12) (4 2 )(1/11 3/11
3/11 −2/11)2 .6364
=(1 /11 3 /113 /11 −2 /11)
q3=−(4 2 )(1/11 3 /11
3/11 −2/11)2.6364
=
(−0.3448 −0 .2759 )
r3=−(1 /11 3 /113 /11 −2 /11)(12)
2 .6364=(−0.24140.0 .45 )
A3−1=( 1 /11 3 /11 −0.2414
3 /11 −2/11 0.0345−0.3448 −0.2759 0.3793 )
Número 4
A=(1 1 1 12 −1 1 −23 −1 2 5
−1 2 3 4)
A1= [a11]=1
A1−1=¿¿]=1
Segundo paso
A2=(1 12 −1)
u2= 1
v2=2
a22=-1
∝2=-1-1.1.2=-3
P1=1+1.2.1 .1
−3 =13
q2=−1.2−3 =
23
r2=−1.1−3
=13
A2−1=(1/3 1/3
2/3 −1/3)Tercer paso
A3=(1 1 12 −1 13 −1 2)
u3= (11)v3=(3 −1 )
a33=2
∝3=2-(3 −1 )(1/3 1/32/3 −1/3)(11)=1/3
P2=
(1/3 1/32/3 −1/3)+
(1/3 1/32/3 −1/3)(11) (3 −1 )(1/3 1 /3
2/3 −1/3)1/3
=(1 31 1)
q3=−(3 −1 )(1/3 1 /3
2/3 −1 /3)1 /3
=(−1 −4 )
r3=−(1 /3 1/32 /3 −1/3)(11)
1/3=(−2−1)
A3−1=( 1 3 −2
1 1 −1−1 −4 3 )
Cuarto paso
A4=(1 1 1 12 −1 1 −23 −1 2 5
−1 2 3 4)
u4= ( 1−25 )v4=(−1 2 3 )
a44=4
∝4=4-(−1 2 3 )( 1 3 −21 1 −1
−1 −4 3 )( 1−25 )=-65
P3=( 1 3 −21 1 −1
−1 −4 3 )+( 1 3 −21 1 −1
−1 −4 3 )( 1−25 ) (−1 2 3 )( 1 3 −21 1 −1
−1 −4 3 )−65
=
( 0.5385 0 0.07690.8154 −0.2 −0.1692
−0.3231 0.4 −0.0462)q4=
−(−1 2 3 )( 1 3 −21 1 −1
−1 −4 3 )−65
=(−0.2308−0.09230.3385 )
r 4=−( 1 3 −21 1 −1
−1 −4 3 )( 1−25 )−65
=(−0.0308 −0.2 0.1385 )
A4−1=(
0.5385 0 0.0769 −0.23080.8154 −0.2 −0.1692 −0.0923
−0.3231 0.4 −0.0462 0.3385−0.0308 −0.2 0.1385 −1/3
)
