Download - Tarea de Practica Calificada 1 Mate Discreta
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
1/8
SOLUCIONARIO
CICLO:2015-I
CODIGO:CB-112 U,V
DOCENTES:JOSE BENITES,JOSUE ANGULO
PRACTICA CALIFICADA N°1
2.-Just!"#$%& su '(s)u(st# '*u'&s#+($t( %(t('+$( # ('%#% & !#s(%#% %( #s
#!'+#"&$(s s*u($t(s:
# S A (s +#t'/ $('t(, ($t&$"(s A-1 (s $"#.
S&u"$:
S#(+&s 3u( )#'# 3u( u$# +#t'/ s(# # $('s# %( &t'# %(( "u+)' 3u( ()'&%u"t& %( #+#s s(# *u# # # +#t'/ %($t%#% 4I.
D#t&s:
• AB6BA6I
• AC6CA6I
S:
BA6I s ( +ut)"#+&s # +#t'/ C # #+&s '(sut#'7#
8BAC6 8I C t&%# +#t'/ +ut)"#%# )&' # %($t%#%, '(sut# # +s+#
8BAC6C9 81
S:
8BAC6B 8AC #)"#$%& # )'&)(%#% "&$+ut#t# ($ ( )'&%u"t& %( +#t'"(s
B 8AC6B8I s#7#+&s 3u( 4AC6I
B 8AC6B9 82
S($%& 4I # +#t'/ %($t%#%
)('& t&%# +#t'/ +ut)"#%# )&' # %($t%#%, '(sut# #
+s+#
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
2/8
D( 81 82 s( %(%u"(:
B6C
P&' & t#$t& # $('s# %( u$# +#t'/ (s $"#.
√ 6 (s ''#"&$#
S&u"$:
Su)&$*#+&s 3u( √ 6 s(# u$ $+('& '#"&$#. S#(+&s 3u( &s $+('&s
'#"&$#(s s&$ %( # !&'+#:
p
q S($%& 4) 43 )'+&s ($t'( s
;S:
√ 6= p
q → p=√ 6 q
p=√ 6 q → p2=6 q2
C&$"u+&s 3u( p2
(s +t)& %(
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
3/8
6 k 2=q2
C&$"u+&s 3u( q2
(s +t)& %(
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
4/8
% >u( &)('#"$ #'t+=t"# ($ "&+)(+($t& # %&s '(#/# )#'# "&$('t' :A,B,C,D,
9,? # +$s"u#s
(
@.-D#%# # +#t'/
A=
[10000010 10000000 10000011
10000001 10000001 1000000010000000 10000010 10000001]
D&$%( #21 #@2 (st$ %#%#s ($ !&'+#t& s*$&-+#*$tu% &s &t'&s ((+($t&s ($
("(s& 2$-1, ##' # su+# %( &s ((+($t&s %( # %#*&$# )'$")# %( # +#t'/ A-
1. R(#/#' +&st'#' &s ""u&s ($ ("(s& 2$-1.
S&u"$:
;S*$& +#*$tu%:
• #21 610000001 6 −0000001 6 -1
• #@2 610000010 6 −0000010 6 -10
; E"(s& 2$-1:
• #116 112-1 6 10000010
11 10000000 6 10000010
11 6 00000010 610
11 6 10
• #12 6 12 2-1 6 10000000
12 10000000 610000000
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
5/8
12 600000000 60
12 60
• #1@ 6 1@ 2-1 6 10000011
1@ 100000006 10000011
1@ 6 00000011 611
1@ 6 11
• #22 6 22 2-1 6 10000001
2210000000610000001
2260000000161 2261
• #2@ 6 2@ 2-1 6 10000000
2@ 10000000 610000000
2@ 600000000 60
2@ 60
• #@1 6 @1 2-1 6 10000000
@1 10000000 610000000
@1 600000000 60
@1 60
• #@@ 6 @@ 2-1 6 10000001
@@10000000610000001
@@60000000161 @@61
C&$ t&%&s (s&s "#+&s $u(st'# +#t'/ 3u(%#'7# %( # s*u($t( !&'+#:
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
6/8
A=[10 0 11
−1 1 00 −10 1 ]
##'(+&s su +#t'/ $('s#:
P'+('& ##'(+&s su %(t('+$#$t(:
%(t A6 10 811 - 8-100 H 0 8-11 800H 11 8-1 -10 801 H%(t A6 10 8 1 -0 0 11 8 10 - 0 %(t A6 10 0 110%(t A 6 1000
Lu(*& (s"'+&s # +#t'/ t'#$s)u(st# %( A, # '()'(s($t#'(+&s )&' AT:
A ¿
[10
−1 0
0 1 −1 011 0 1 ]
Lu(*& ##+&s # #%u$t# %( AT:
• C&!#" A 11 6 811 8-10 0H
C&!#" A 11 6 81 0 6 1C&!#" A 11 6 1
• C&!#" A 12 6 - 8 0 1 8-10 11H
C&!#" A 12 6 - 8 0 110 6 -110C&!#" A 12 6 -110
• C&!#" A 1@ 6 8 0 0 81 11H
C&!#" A 1@ 6 80 11 6 -11
C&!#" A 1@ 6 -11
• C&!#" A 21 6 - 8 -1 1 80 0H
C&!#" A 21 6 - 8-1 0 6 1
C&!#" A 21 6 1
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
7/8
• C&!#" A 22 6 8 10 1 80 11H
C&!#" A 22 6 810 0 6 10
C&!#" A 22 6 10
• C&!#" A 2@ 6 - 8 10 0 8-1 11H
C&!#" A 2@ 6 - 810 11 6 -101
C&!#" A 2@ 6 -101
• C&!#" A @1 6 8 -1 -10 81 0H
C&!#" A @1 6 810 0 6 10
C&!#" A @1 6 10
• C&!#" A @2 6 - 8 10 -10 80 0H
C&!#" A @2 6 - 8-100 -0 6 100
C&!#" A @2 6 100
• C&!#" A @@ 6 8 1 10 8-1 0H
C&!#" A @@ 6 810 0 6 10
C&!#" A @@ 6 10
L# #%u$t# 3u(%#'7# #s7:
#% A ¿[
1 −1 10 −111 1 0 −10 1
10 10 0 1 0 ]
L# $('s# '(sut#:
A-1¿
1
det A #% A
-
8/17/2019 Tarea de Practica Calificada 1 Mate Discreta
8/8
A-1¿
1
1000 x [
1 −110 −111 10 −101
10 100 10 ]
Su+# %( # %#*&$# (s:
D#* A-161
1000+
10
1000+
10
1000=
101
1000