Sistemas ineales ExamEn dE EnERo 2004 1. (2 pt.) En el sistema

"!#$ %'&)(+*,*./10243658790;:=<?>A@CB'DFEGDH7H@CI6J6KMLN@DH@IL8@CDH7HOJJQPSRT>U7FEG>ML8JVP9ECTWR >XDH@YOF@CJVBZE\[CJ6L8>^]_B\7HO`JVaNR5_JVDHRVbJdceR
aN@YL_>8JDH@U>8f JVB PSRT>U7FEG>ML8JL8DFJV>_aNR5_J1OJg@CBGBGRL_>=]_B\7HOFR5_JVDFRVb_JdceRQa8EGDFPSOF@97HRN0
m,npoUq
m l 2jiF: rs
k npoUq
kUl 2jiH:
k 2jiF:
2jt?:
v
r
u
4
2
x
w
:
m 2jiH:
C/D
D/C
h 2jiF:
y J6DH@U>8f JVB aN@@C>U7HOJVa8J k j2 iF:{zMEG@C>[email protected]|DFL=7HO`JV>8DH}jRVOIJVa8JgaN@~8RTLNOE\@9O|€2jt?:`
‚„ƒ†…‡
1
…
?
…
‰
…‰dŠŒ …‰
ˆ
ˆ …‰‹ŠŒ
y JgDF@U>8f JVB h 2jiF:?@CD|L8>7HOF@C>ŽaN@aN@CBG7FJVD@CKUL_E\@CDH5_JVP9EGJVa_JVD{Y0$<B+b_B\RKMLN@Y‘|’‹“”@CD|L8>vPSRT>•zV@9O`DHRVO
PSRT>U7FEG>UL8R1–—a8EGDFPSOF@97HRKMLN@|7HOJV>8DF}˜RVOI6JBGJVD{aN@CB\7FJVDPSRT>U7FEG>ML8JVDš™U2jiF:@CD{EGIg5L8BGDHRTDa8EZDFPSOF@97HRTD?™ n ›.qœ
aN@7FJVBNIgRaNRKMLN@DH@P9L8Ig5_B\@KMLN@ k n ›.q+ž k 2 › Ÿ:`0<BMb_B\RKMLN@{“’V‘ O@CJVBGE\[CJŸBGJ7FJ1OF@CJEG>UzV@9ODFJ œ
5_JVDFJ1OaN@EGIg5_L_BGDHRTD{a8EGDFPSOF@97HRTD|™ n ›.q JgaN@CBG7FJVDPSRT>•7FEG>ML8JVDx™M2jiF:`0 y JgDF@U>8f JVB,aN@@C>U7HOJVa8J k 2jiF:{DH@
ILN@CDH7HOF@CJQJgBGJ}˜O@CP9LN@C>8P9EGJgaN@¡x¢KUL_EGDH790
2†J•:Ž‘šJVBGP9L_B\@Ÿ„¢va8E\b_L‹cH@@CB,@CDH5.@CPS7HOFR6aN@ kMl 2jiH:`0
2jb+:“ŸE\b_L‹cH@ 24w:2†BGJg£¤OJV>8DH}jRVOIJVa8Jga8@~NRTLNOE\@9OaN@BGJgDH@M>8f JVB k n ›.q :`0
2†P¥:Ž¦E,DH@aN@9]_>N@BGJ7HO`JV>8DH}jRVOIJVa8JgaN@~8RTLNOE\@9Oxa8@ m.n ›.q PSRTIgR
­ w ­M¯±°
§ 24wx: ž©¨”³
ª ²C 24wx: ­« s=w ¬®
­M¯ « s
a8E\bL‹ce@Ÿ@CB,]B\7HOFR rvu 24wx:{¢vBGJgDH@M>8f JVB § l 2jt?:`0
2†a:=¦E rs 2jt?:@CDL8>´]B\7HOFR5_JVDHRVb_JdcHRŽPSRT>µ}jOF@CP9LN@C>8P9EGJvaN@gPSRVOF7H@6t ‰ P9JVBGP9L8B\@gBGJOF@CDF5_LN@CDH7FJ
JVB EGI5_L8BGDHR¶TB\RVb_JVB·aN@CB,DFEGDH7H@CI6Jg@C>=@CB aNRTI6EG>8E\[email protected]
3M0243 œ¹¸ 5_790;:º>_JDH@M>8f JVB,PSRT>U7FEG>ML8J
DFEG>,2 ° iF: ¯ i ¬ /1¼ ¸
k u 2jiF: ž»¨
OFª @CDH7HR
ª
@CDBGJ@C>U7HOJVa8J=JvL8>µDFEZDH7H@CIJ y £½PSRT>´OF@CDF5_LN@CDH7FJvJVBEGIg5L8BGDHR k s 2jiH: ž ¿ ¾ ™M2ji?Ã#/1¼ ¸Vo :`0
À9Á¤Â
“@C>NRV7FJ1OF@CIgRTDBGJgDFJVBZEGa8JaN@CB [email protected] k 2jiF:`0
¾
/
†2 J•:v“ŸE\b_L‹cH@BGJVDDH@M>_f JVB\@CD k u 2jiF: œ k s 2jiF:{¢ k 2jiF:`0
2jb+:=‘šJVBGP9L_B\@BGJ7HOJV>8DF}˜RVOI6JVa8JgaN@~NRTLNO`E\@9OxaN@ k 2jiH:`0
2†P¥:Ž‘šJVBGP9L_B\@BGJŽDH@M>_f JVB$aN@6DFJVBZEGa8J m 2jiH:ŸP9L_JV>8aNR k 2jiH:@CDBGJ=@C>U7HOJVa8JŽJ^L8> >MLN@9zVR y £½PSRT>
OF@CDH5LN@CDH7FJJVB EZIg5_L8BGDFR
r 2jt?: ž©¨ u ­ tt ­M¯±°
­ ­
±°
ª
M0243 œ¹¸ 5_790;:‘{RT>8DFEZaN@9OF@Ÿ@CB DFEGDF7H@CIJgaN@BGJ]8¶TL8OJ
.
¦J1b_EG@C>8aNRYKMLN@ u n ›.q @CD{L8>DFEGDH7H@CI6J y £ ½$P9JVL8DFJVB.KMLN@x7FEG@C>N@L8>Q5.RTB\R@C>"! u ž ¼ ¸ ¢L8>PS@9OFR
ª
@C>#! ž ¼¹3 ¸Mœ ¢
ª
/
s n ›.q+ž%$
n ›.q
'&)(+*
†2 J•:v“@97H@9OIEG>_J1OxBGJ@CDH7FJ1b_EZBGEGa8JVa=aN@CB,DEGDH7H@CIJ0
2jb+:=‘šJVBGP9L_BGJ1O@CB a8EGJ1¶VO`[email protected]\RTDš¢vPS@9OFRTDxa8@CB DFEGDH7H@CI6J0
2†P¥: ,b87H@C>8@9OxBGJOF@CDH5LN@CDH7FJgJVB EGI5_L8BGDHRaN@CB DEGDH7H@CIJgEG>UzV@9ODHRP9JVL_DFJVB40
02e/Q587`:º> ]_BG7HOFRŽ5_JVDHRVbJdceRXa8EGDFPSOF@97H/
R u n ›.q 7FEG@C>[email protected]>_DH}˜RVO`IJVa8JŽaN@~NRTLNOEG@9O rvu 24wx:`0
º>=5.@9OE\RaNRgaN@a8EG1P 08JgDH@M>8f JVB,7FEG@C>N@BGJ}jRVOIJ
r=u 24w:
w
à °
°
‘šJVBGP9L_B\@¢a_E\b_L‹cH@ r s 24w: œ DFE\@C>8a8R2 s n ›.q+ž 2eÃ/¥: u n ›.q 04365ŸL{YW@ P9BZJVDH@aN@]_BG7HOFR@CD7 s n ›.q 0
¸ 024358790;:6¦M@z1JgJg58OFRPS@CaN@9OxJVB,@CDF7FL8a8E\RgaN@YL_>v5_L8BG( DHROF@CPS7FJV>8¶TL8BGJ1O9882jiF: œ aN@9]_>8EZaNRPSRTIR
­ i ­M;
¯ <s
882jiF: ž©¨;:
i ­ ;< s
­
ª
2†J•:v“ŸE\b_L‹cH@@CB I±TWR a_L8B\RgaN@BGJ7HOJV>_DH}˜RVO`IJVa8JgaN@~NRTL8OE\@9OxaN@ 882jiF: œ ­ = 2jt?: ­ 0
2jb+:=¦M@|ILN@CDH7HOF@CJ = 2jt?:'PSRT>L8>7HOF@C>a8@|aN@CB\7FJVD @CKML8EGa8EGDF7FJV>•7H@CD ?t > œ a8JV>8aNRBGL8¶TJ1O$JBGJDH@M>8f JVB
¾ = 2 o t?:e™M2jtà o t > :
À9Á¤Â
“ŸE\b_L‹cH@ = l 2jt?:{5_J1OJ ­ t ­¯BA P9L8JV>_aNRtC¾ >z1JVB\@ s œ s s ¢ s 0
2†P¥:v“ŸE\b_L‹cH@?BZJx}†L8>8P9ECTWR >[email protected]<BE« 8 l 2jiH: 5_J1OJP9JVa8JŸL8>NADR< « aN@š< «B\RTD·z1JV< « B\RVOF@CD aN@{tC>?aN@CBMJ15_J1OF7FJVaNR
JV>U7H@9OE\RVOC0
=
l 2jt?: ž t
@
>
3