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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