ALGEBRA LINEAL PC 2 Con Clave 2019-I

 

ZLKYJRXKFEF LEHKGLEA CE[GR FJ XEL CERHGX

(Zlkvjrskfef fja Pjrÿ, FJHELE FJ ECÄRKHE) IEHZAVEF FJ KLNJLKJRÃE JAJHVRØLKHE [ JAËHVRKHE Prehtkhe Heakikhefe 2 - 205;-K HZRXG PRGIJXGR

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EANJBRE AKLJ AKLJEA EA Cn. LGAEL OERE OERE

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EPJAAKFGX [ LGCBRJ? WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW Klstruhhkgljs? Ags jxåcjljs quj utkakzel aåpkz y/g akqukf pepjr lg tkjljl fjrjhdg e rjhaecg. Prjnultes? 5)  Fjtjrcklj sk aes sknukjltjs prgpgskhkgl prgpgskhkgljs js sgl vjrfefjres g ieases, oustkikquj su rjspujste k) Xk ae cetrkz huefrefe B lg js klvjrtkbaj, jltglhjs Xgauhkøl.

30

js ul veagr prgpkg fj ae cetrkz B.Y B. Y

Xebjcgs quj ae cetrkz B lg js klvjrtkbaj hhuelfg uelfg fjt(B)30, pjrg?   js ule , jltglhjs P(0)3fjt(B)30, ag huea qukjrj fjhkr quj reãz fja pgaklgckg herehtjrãstkhg, pgr ag teltg hglstktuyj ul veagr prgpkg fj B .

 3 fjt2 5 0 30  3 ]80 20 06S  3 59    2   5 0 0 3  3  80 2 0  66 0  3 6    6 + 5   3   3 59 −    3   − − − −  | 3 |   | 3 |   | 3 | |   | | 3 |  | 3  3 |  5 0   ; 4  3 000 500   5>0 9:5 5 0   ; 4 0 3  0 0 05   50> 95 :  →  33  5 , 5  , jltglhjs

kk) Xk

 js ul veagr prgpkg prgpkg fj ae Cet Cetrkz rkz B². Y

Xgauhkøl.   Xgauhkøl.

Xebjcgs quj, sk  js ul veagr prgpkg fj ae cetrkz B , jltglhjs js ul veagr prgpkg fj B² . Jstg lgs pjrcktj heahuaer fkrjhtecjltj ags veagrjs prgpkgs fj B  y e pertkr fj jstgs veagrjs heahuaer ags veagrjs prgpkgs fj B² ?

 ,  ,

ag teltg

 6

js ul veagr prgpkg fj B, pgr

 js ul veagr prgpkg fj B²

.

kkk) Xk E js sjcjoeltj e B, jltglhjs sus pgaklgckgs herehtjrãst herehtjrãstkhgs khgs sgl knueajs. Y Xgauhkøl.

Xk E js sjcjoeltj e B , jltglhjs jxkstj ule cetrkz P tea quj

  , pgr ag teltg?

 

ku) Xje

, jltglhjs ags veagrjs herehtjrãstkhgs fj B sgl? 4, -4, 5 y -5. I

Xgauhkøl.

 

 

? ?    →       +  ++ ² 3 8  2 + 8  2 +: + :²²   5  35       3       5 3 8+ 8 + 2 + :²:² ≠ 5   5

2) Xje

ule trelsigrcehkøl akljea fjiklkfe pgr   Jltglhjs js hkjrtg quj? (oustkikquj su rjspujste) k)   js ul vjhtgr prgpkg fj V hgrrjspglfkjltj ea veagr prgpkg

 I 

Xgauhkøl.

Xk fkhdg vjhtgr js herehtjrãstkhg, fjbjrãe hucpakrsj quj   , pjrg?   kk)  Ae rjprjsjltehkøl cetrkhkea cetrkhkea fj V rjspjhtg e ae besj helølkhe js fkengleakzebaj. Y  Xgauhkøl.

 | 3 802 802 : 00  3 :  ²5     3 ] 80 2 082 0:0S → 0 3 |  0   5  3 : → {(50 ) (05)}

 

= E js fkengleakzebaj. 

kkk) 

Ae cetrkz

Xgauhkøl.

5; ; 9  3 ]2:5> 55; 6;S

  lg js fkengleakzebaj. fkengleakzebaj. Y 

5;   ; 9 2   3 5 → ]54]2:545> 352;;  52>:;9: ⋬⋬ 5500;S ~]005 6800; 5 60→ ⋬⋬3 005S →, 28  3 63 3 6  3 6 3  (86)   8 8 8  

 

    3 2  2=,  3 ]862]6 202 682S6S   (0)  ]6 2 6 ⋬ 0S3 ]52 5 2 ⋬ 0S  2 26 52 26  3 3 00  → 26 52 26 ⋬⋬ 00  ~ 00 00 00 ⋬⋬ 00  →  3 22 2  3 2 2   5   →   3 ]28  S ¸

kv) 

Ja subjspehkg fj R¸

  hgrrjspglfkjlt hgrrjspglfkjltjj ea ve veagr agr prgpkg

  js ul jspehkg herehtjrãstkhg fj .Y

Xgauhkøl.

 

 

8) Hglskfërjsj ja gpjrefgr akljea V?R¸ R¸ tea quj V(T)3ET, fglfj

trjs vjhtgrjs prgpkgs fja gpjrefgr akljea sgl? u3(0,5,5)= v3(5,-5,0) y w3(5,0,-5) k) Fjtjrcklj ae rjnae fj hgrrjspglfjlhke fj V . kk) Gbtjlne ae fkcjlskøl fja Mjr(V) . Xgauhkøl.

 yT

. Ags

 

  0 5    + +  0 0  3  → ]28  S 55 3  55 → ( +++ ) 3 () 5        5 5      3  → ]28  S (50 ) 3  (50) → (  ) 3 (  ) 5     5           + 33→,, → → 3]8233,  →→S 53++05 ,33 (→03) →,+ (3+)→ 3 (+,03+) 3  →    3  →  3 ,,  3 ,,  3 5,,5 3 5 → 3 ,,  + 3 ,,+ 3    3 3 ]28 68 28S  3 3 ( ++  ++ )  

 

 

 

 

 

 

k) k)  

kk) kk)  

 

     +        + ) 3 () →  3 , 3  → ( (  ) =  ∄    3 3 () → ( +  +    +  + +   