Ejercicios Resueltos Transformacion Lineal

March 16, 2023 | Author: Anonymous | Category: N/A
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S]NE_@G]HNOBßE JBEFNJ S]NE_@G]HNOBßE FDF]OBOBG_ ]F_VFJSG_ >.  _fn H uen hntrbz quf cf`bef uen trnes`grhnobÿe jbefnj fetrf jgs fspnobgs vfotgrbnjfs F y F‘ fe jns mnsfs mnsfs oneÿebons y sfn E uen hntrbz quf bkunjhfetf bkunjhfetf cf`bef uen trnes`grhnobÿe jbefnj fetrf jgs fspnobgs vfotgrbnjfs F y F‘ fe jns  mnsfs grcfencns M cf F y M‘ cf F‘, cfhufstrf quf nhmns n hmns hntrbofs cf`befe c f`befe jn

hbshn trnes`grhnobÿe jbefnj sbe cftfrhbenr jn `ÿrhujn cf jn hbshn.

             *   + *     +                     ⁃ ⁃ ⁃                       ⁃ ⁃ ⁃                 ⁃ ⁃ ⁃             ⁃⁃  ⁃⁃  ⁃⁃      ⁃⁃ ⁃⁃ ⁃⁃    ⁃⁃  ⁃ ⁃  ⁃ ⁃      ⁃ ⁃ ⁃      ⁃⁃   ⁃⁃   ⁃⁃         ⁃   ⁃   ⁃      H8

 , E 8

vfotgrbnjfs

 y

M8

  cf`befe trnes`grhnobgefs jbefnjfs fetrf jgs fspnobgs

 

  y M‘ 8

 

_gjuobÿe4 M‘ 8

 , , M 8

 

 

 

 

 

H y E sge sfhfdnetfs, cf`befe jn hbshn trnes`grhnobÿe jbefnj

Vebvfrsbcnc cf Onrnmgmg @noujtnc cf Bekfebfrèn Cfpnrtnhfetg cf Hntfhîtbon

\rg`. Egrfjye _uîrfz Njkfmrn Jbefnj

 

 

     *  +  *+                                                     ↝ ↝                                     ↝      ↝                                                   .  / ↝ .  /↝ ( |⁃ ⁃)  ↝ ( |⁃ ⁃ ) Y⁃ ⁃ X                Y⁃⁃ ⁃⁃X              =.  _fn 4

 jn trnes` tr nes`grhnobÿe grhnobÿe jbefnj cf`bebcn pgr  y sfne M8  y   yy  rfspfotbvnh fspfotbvnhfetf, fetf, M‘8   cgs mnsfs grcfencns cf  y  r  cgs ogesbcfrf n C y C‘ oghg jns  mnsfs oneÿebons oneÿebons cf oncn fspnob fspnobg, g, anjjf n   yy    

 

_gjuobÿe4

)

 

(->, ?,-3) 8

(>, >,, >,>)+

(6, >, >=) 8

(>, >,, >,>)+

(>, )

 

 

 

 

,

8

 

 

, \8

,

Vebvfrsbcnc cf Onrnmgmg @noujtnc cf Bekfebfrèn Cfpnrtnhfetg cf Hntfhîtbon

 

,

 

\rg`. Egrfjye _uîrfz Njkfmrn Jbefnj

 

 

                              *  + *+    ⁃ ⁃ ⁃ ⁃ ⁃          ↝               ⁃ ⁃ ⁃ ⁃ ⁃              ↝           ↝   ⁃ ⁃   ⁃   ⁃ ⁃     ⁃⁃  ⁃ ⁃ ⁃ ⁃   ⁃⁃ ↝  ⁃⁃   ⁃⁃       ⁃⁃   ⁃⁃         ⁃      ⁃   ⁃   ⁃   ⁃   ⁃   ⁃      ⁃ ⁃ ⁃      ⁃ ⁃ ⁃  

  jn trnes`grhnobge jbefnj quf sf gmtbfef cf jns hntrbofs cf ?.  _fn 4   hxe cncns oghg jn rfprfsfetnobÿe fe jns mnsfs usunjfs. Feoufetrf jn `ÿrhujn  pnrn oncn uen. uen.   cf

 

_gjuobÿe4

(>,, @>8

 

@?8@?+?@> @?8@?+?@>

@=8 @= @=8

@?8@?-3@= @?8@?-3@=

@?8 @? @?8

 

 m8  m8

 

c8 c8

 

o) oghprufmf su rfspufstn onjoujnecg

 

cc8 8

 

 

 

, =8 ,

8  

 

 

c cbrfotnhfetf.

_gjuobÿe4

@=8@=+0@> @=8@=+0@>

@>8 @> @>8

 @=8 @=  @=8

@?8 @? @?8

8  

@?8@?-3@= @?8@?-3@=

 

,

 

,

8

,

 

,-    ⁃⁃  c8

 

 

 

Vebvfrsbcnc cf Onrnmgmg @noujtnc cf Bekfebfrèn Cfpnrtnhfetg cf Hntfhîtbon

\rg`. Egrfjye _uîrfz Njkfmrn Jbefnj

 

 

c) feoufetrf jn hntrbz cfj onhmbg cf mnsf cf C n M, oghprufmf quf uen fs bevfrsn cf jn gtrn. _gjuobÿe4

                ⁃   ⁃ ⁃             ⁃    ⁃ ⁃           @>8 @> @>8

 

@?8@?+?@> @?8@?+?@>

@=8 @= @=8

 

 

@>8@>-@=, @?8@?-3@=

 

   ⁃⁃     ⁃⁃   ⁃⁃         ⁃             ⁃      ⁃ ⁃⁃      ⁃ ⁃ ⁃      ⁃⁃   ⁃⁃    ⁃⁃      ⁃⁃   ⁃⁃     ⁃⁃   ⁃ ⁃   ⁃⁃   ⁃⁃    ⁃⁃    ⁃⁃     ⁃ ⁃                   ⁃ ⁃   ⁃ ⁃    @?8 @? @?8

 

@>8@>+ @?, @=8@=-?@? @>8@>+

 

^8

,

8

Vebvfrsbcnc cf Onrnmgmg @noujtnc cf Bekfebfrèn Cfpnrtnhfetg cf Hntfhîtbon

 

\rg`. Egrfjye _uîrfz Njkfmrn Jbefnj

 

 

**++                     

6.  _b M8

  fs

M‘8

uen

  

  fs uen mnsf grcfencn cf , mnsf grcfencn cf   y

  cf H?x3, feoufetrf uen `ÿrhujn pnrn

H (

                                                                                                            (x,y,z,w).

_gjuobÿe4

=(>,>,,) ‟  3(,>)8  3(,>)8 (0,-=,,>,)8 (3,0,=)

>,>,,(>,) + )8 (;,0,>)

(,>,>) 8 ->(>,>,(,>)8 (->,) @?8@?-@> @?8@?-@>

 

@38@3-@= @38@3-@=

@?8-@? @?8-@?

 

 

@>8@>-@?, @=8@=-@?, @38@3+@? @>8@>-@?,

 

@38-@3 @38-@3

@?8@?+@3, @=8@=-=@3, @>8@>-@3

 

 

(x,y,z,w)8 (w+x-y)(0,-=,) + (y+z-w-x)(->,) (y+z-w-x)(->,)

(x,y,z,w)8 (0x-0y+0w, -=x+=y-=w, =w, =x-=y-=z+3 =x-=y-=z+3w) w) + (;y-;w, 0y-0w, y-w) + (-y-z+w+x ( -y-z+w+x,, >x-3y-6z+1w, 3x+=y-0z+3w, 3x+=y-0z+3w, x-z+=w)

Vebvfrsbcnc cf Onrnmgmg @noujtnc cf Bekfebfrèn Cfpnrtnhfetg cf Hntfhîtbon

\rg`. Egrfjye _uîrfz Njkfmrn Jbefnj

 

 

  

\rgpufstgs ;.=

↝  jn trnes`grhnobÿe jbefnj quf sf gmtbfef cf cgs hntrbofs cf hxe cncg oghg jn _fn Ñ4 rfprfsfetnobÿe fe jns mnsfs usunjfs, anjjf jn `ÿrhujn cf jn trnes`grhn trnes`grhnobÿe. obÿe. ❵ 

   

  Mnsfs

{(>,,= m= + γ>? m?  

Ñ () 8 γ=> m> + γ== m= + γ=? m? Ñ (>,,,,= ()  

   ,-   

8

 8

 

Ñ (x,y) 8 γ> Ñ (>.,3) + R ()

,-   8

 

Ñ (x,y) 8 (?x, x, 3x) + ( ,
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