aducerea cuadricelor la forma canonica

9
Ju*'ntu'\ lortro & /trf,*j* ,*tA#'-*A4 X- W #s'ffirY.o'*' t et*l;o ,X^uuk o t'nw' *'*d''* "*fi ' JU e,,r't %lz* es3f* sa, x/* z%t\u' tqt{e + Lq+x r h.+ ll Z\rzn 2:=^o *d, xt | 1* ,*,{ *d*"/il ltf'/ilr} f* e/'k'a'tl & l' o'd-^"e * ,^J-***A '?/' / Tu A = {Q,, I fQrc f t a/b \ *N:, OMl efd#* ff*, /,*) J Qrz o,b i Qzz Qery / -Af ezz {r3 / /o = 4,^'r %A? aureT "lr;/, *,rou, **Jr o u,/ rryolr * h>+2 * Q*+ I t A = A- ^o J*i-s Y 1d ul Jo L J'-# i.

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Page 1: Aducerea Cuadricelor La Forma Canonica

Ju*'ntu'\

lortro &

/trf,*j* ,*tA#'-*A4 X- W #s'ffirY.o'*'t

et*l;o ,X^uuk o t'nw' *'*d''* "*fi '

JUe,,r't %lz* es3f* sa, x/* z%t\u' tqt{e + Lq+x r h.+ ll Z\rzn

2:=^o

*d, xt | 1* ,*,{ *d*"/il ltf'/ilr}

f* e/'k'a'tl & l' o'd-^"e *

,^J-***A '?/' /

Tu A = {Q,,IfQrcf

t a/b\

*N:, OMl

efd#* ff*, /,*)J

Qrz o,b iQzz Qery

/-Afezz {r3

//o= 4,^'r %A? aureT "lr;/,

*,rou, **Jr o u,/ rryolr

* h>+2 * Q*+

I

t A = A- ^o

J*i-s Y

1d ul Jo

L J'-# i.

Page 2: Aducerea Cuadricelor La Forma Canonica

-z-

Al*Yw"t er,r*J'. /uto&''*u'' ("u/ f*;

\x I i: ).A-l';) rn{"Qu *+\i, td/

/ ' ,yfra_tu aM ,{WWrffi'#fJ W,yj

i I i. '

,strtd, {i/ ';'tfu'rV,v1{

tlz ry A, lt

),xtt / 2ty / 'Ab* -r{/f:#rA

,.Mrc"fi ffr W" L"

o#u''r-'d' '*mre#P'r"{

&'# E'r"r

*u&-/ufr*te )

# \ie i*uoJd$

/

rF\\\

t

\\\

* Q++: c

obw} e

(^' \' u' )A li' | + A = o ' *"il o=11i,',,';,?,: I',nn\ d / [g'l Jrlt,z

r e e,,x'* urrJ') orrr'i,q,i7"o.^'2''znzzl't'';ffi= o E:: ;:';^;,

&fr,r./;- ^M/a"'4 f ,rlwfu- /,'Y*-

il'' n4/**; A W 2,,h,,).

q)olp'rL /hryi , B'= | nt , ntr, AuJ bM ^v>;fu'eu"a/; a '/*' n\

rt,*ta'J: :;-/* #* *y^'^d *n^u #J n4, *,/,& ^fu; &/T= y'

-, /'l*aJ/

,T*-fu**c

U:' ) rff: j

ry&*J,I 'f#,n* nU

'#. * zrl r 2O

,# @ d* * 36 = o

Page 3: Aducerea Cuadricelor La Forma Canonica

*3-

frnfru

Mfr*162t'o

* ZZ x'c#'

i, ' -l-'_;.-J* (xa,yct ro J ? J;+X

?j i{,*, fc,&i ff #.}.; t\.- I l J

(r/ \/

C\T idl- i A* o,!*, &J *. #'\, .t F

<!r #

1 Yno rJ* = 2L

\l- xa f SloG "*, =-/I U-I -2v +'4; =4| -.Jr, ,cc

,r#,to * #yu6

iJ

iI

tLJo- 1*- +%* zf = o

t0 %e 4yo* I *0U

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c

c4

Go*,

-*h ,"ue*#*J e(,*zto)

' l= {-- /c, lxii

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?, xr#e ,o'njq

CrA,/r|, -#*fuu( f;?ffi' r

//

7 P)=*fef f 'Alb)= /::A', l 1

Io

{n' ?' r')-ff;

) + hr o

,{^ Ln#tr.t,

'#&5 i &l= /6 e

,V.)/\/ | *t

I-t af

l* PLtI'-)l l+

o -ll*L 11

€ --4/ nfn _5b

4t6

*L

6-2

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Page 4: Aducerea Cuadricelor La Forma Canonica

\--/r*

rfu-) ){rl-n} (t2) /,ft-})€4(r ^)

=s

{' /i'

r ft z)dhqrh -r'6) 4t€*2) =

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, -0b- rf )'+ eeh -t6z)-- P(7*-rt)r t')

-- 8t2tx3)-rct)=

= - Lr,()-

3)'t rr ( z - t)J= - f' s ) {nf^- s) t r r l':r

: [\- s) / ^. 1>o rt) = - ()-s) (^ z)(z t)

* ),=g, 2r= 3, )z= 6 .*of*# fy"' \ i?r\ lo \

?*1* A,=9 n*ylruY* ouJ**J (4 ''': )(g )=(:/, -n, l

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a=i,\' 'z

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4 .z :)6,1 f) -f!,r!,,i:':":',^:,-4 [-, 3

\o -L

r _-.t

t,^,Fu"'

rg {r 'dL\ S""

Irt#!If

Page 5: Aducerea Cuadricelor La Forma Canonica

*"{"--IIfI

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t/i/

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t

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t0"\? 3-l

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Page 6: Aducerea Cuadricelor La Forma Canonica

1_

7n*{,,,n'7 ,{"o.r#-**ffi { Md'* )r,] ,' {ru}

L r vt zdx

{g j= Y {fd j 'Cur'

ld' = t.

I p' :: *,rt_b

tt1"

il

S -'y "r L #.t/sr/ s

?'

?*)l- ,v" + & fr-ll5u b

il , ri7 lt _-L*rl-lJF'{ F"'- l.'i3U 3

e#ffi*#utr*d

fr; ^u%

tt ;:' ,.-.,, ,f u tl-t rt-.2 +.5

* 'C""

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,,M/fr/

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L,z.x -t +ft{ 4"

0/rAl.*d

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Cr.rj T #-#& mn* t tt

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euL. ,{* Frl z C+ _-'4F

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Page 7: Aducerea Cuadricelor La Forma Canonica

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(r*k)

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7l w

t

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fr.= of)TJ #r:&rtt

dpx=1

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ft/J vn

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Page 8: Aducerea Cuadricelor La Forma Canonica

"*.,r * I *"

r&y*&"' (/ t / \ F

^r a // \ , \.M,-=r

td*''i,) v j {'f,)I

W;*l

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J

I,l

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t{t+--*V'rl A

ri- I u'* # r{,td ffi.1

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n t. 'L*odeuc'a N"itrt'!t.'-n s

L\t + { fr' \*r.Fd {a{ ! *' rtil;\

14,1 L

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ci"lro

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I t} I-G/ttllf I /-"f ttE

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l-^' o / v,f; Gd

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ll1t'\ "* J- \",1

Ir? fid

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Page 9: Aducerea Cuadricelor La Forma Canonica

"tl€*ft-f' +

d

/^t*

'o A. .,-l

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f)1.

X;.*

e Ve

XI7,z

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L- r/\' + L\'r+{-6 o. bd

trGv'f Jfl /=' o(

e) 36 z'' t ,n/6 - Yz

J . L?- = a

-/, G [x''r, *x' n G)'] e p' dil'

r- e (r'r t1'- 't;il'- * = "

td a(u'-,t)'- ,(a- H=cTt^*". fi.o" t'to Aa ) x'/ - xl

J

(r"= J -*,

I ro--k' ' t?.'"-ll; n"*n!" 6s"'- Et"=o

o"| trnt" t,'l'r^/*^k 6d fo*.db