i { (a) tTtrn" ,Y f ^a4f b t - *y f * ( ,2 ,

f b, ^ ,;'11*l ffr + u+/T/e nw*Ler ,{- prL-+t f btle pryber +

'y*W f to

frb"A'(;! "f pNtrd f* t, ), s B ,,,i,t/\t,al frt + 13 ) -ii-hI

, a.t a iurl6,n^r*r*t 4z+;1,"^a

i ! j l k_! 0-r j -p)!

X r = t f t n [ ^ t , X r = j+'> {art 3 ar,t( zA bt/\ p*A;L'y

F*W uool

p*bl;tjp*W;tt7 i ,,'4

t' a'*/

7 !bi*jr'(rf;"

Lh) TLz

t r&

r:C) %-v ot

f t x , =J l=

r P "+ jt 7 ) { l -i / j J ( + - t j , l

G ) ' ( t -P . ' i7 )(+ - j ) l

T/bef* , tLz cn^ b" WY t * t = t , X > = j , x ) = k 1 =

@,x\ ItQ ffi aA

r*r , a i-j a"t - - *1

f t X r = i , X r = J l :

aLrw> !

7 !

5,tS lu{nP" (*,

. A

) = &'- e. -ol

/L ,l

' Tr , ) t2 , Xa)

A > o r l ,

It/" xn !

7 4 ! x r ! 4 l z s ! t Z

, , x>, z?

r l

U/ta.^e t\ = 74 + N>+Z> t 4

6.tf Lf +k F * dt-vw t1;l/ ,-url.s ,'(/4.n larc1 =1

b UtPt+1-- ' )=?

l : [ rn>= n ) ' ( ) P^ t ' - P f - "ELuu l= M PVAPluc+ t) = tvF( I-f)

La)u v t w w ? Y

Jr*, ,J )=dft [h #lt# f r )

] = x + Y *+y' n -^ Y= \/V-urr/r II UIr w )I V - -I t \ [ - Z

T/ar"l'""i

J M , z ) ='L-

( t->lI

fr,r(3 ,w)= lJ-,, ) fr,y13,,

, Y(r+1r'frrv)= E Jffi;(*,o)dr^

' J t f .y t x ,3) =/)

t * ra); f€ (# +ut) ?-= ,(^, a

6"cto t^ ) L"*

A=Y= AxO Oo o1 Or l

rn1 =ItltlfllltlI

)

[ :

t " ' o

t t r t -x 'JI E ty l+Et" , ]I e [x , ) +ef t r )\ ELxv ]

{ Yt?l tr* Y =

k , = VABlnr,) b+r= VAfih, -kn =hTfx,, x). 4 )

Ky : A KxArKu

K,, t k,rl ( , , t Ktz K , , * K t t K,, t 'Kty

Krt * Krz+kt ll|, KrrtK, rkB tkt K t tF* tkv tFu/K'r tb>t lr + huvkwt F+r + b-v, k+r+ by> p+ > -t Frr| =VAnx , l h , , UAR fx"J

qa^L tut A) a..r( cL ) , )*t eet L,, = Ln S+--hr,=-..:l

X2 ,u M(0, t) Xl (\, /V(2, 4)

r?

= - /

00

1 )6,9s L0)

7 : l0 + )

*

? TIIII)

f 0 + f,l - 2l : 1 o oIl -l . o _ ? +

f t ol o tt o o z= i o n

l - tl t n\ =

o o 1, 2 l

o

N ( 1 ,

t+t :X, cl-'/

It0t ) L/i r x =

T/'a qfo/,va,{^/z . t K ">t =-A>: | .-r\e= )uo l+ l

f ol nl =l f rl -\

KY )3 ,

f 5 ' T ), (; +J /^ ' N ( w t ,

_ t"T /^ A/ap* H =

Ky- o 7,j

Kr= [ ;

L e ) r t v ? Al - f ) m y

X r - f Y r , x ,

!Y1 -- 7v1 xzf H"

r t ;14 L:" . ' ) )? 0

\z - o

' --

j x z

t r -

_l

- 2xr(x, , x l ) z\ , , f , 2,* , ,ar) x. :

[ o r o ) t f ] - ' [ _ o , o J( i J= l'b f * , x> - f a , , x> rv N ( o , l )

d ' / t ELxr')= f , # p.,yntlv') | fr_=o

= =e l - e /x)urpr, :^l"r-QP,ilr+ w,\) - ) fuiz,t'u,wr$1 ,*, >", )) I

= e l @ ' - o; r , , , r r r - - ' ( i t ' - w,2q -wr7, r ) h , (6r l r_-

= +t L 2,' * U-, - cu, Zt- wi,. Yl 't' / J fx,,1 ( 6)la _=

*ltu tA':- h)t;u - (4'z')'t,1-,-w,z>,-t4 >,,)-2,,)- 2 1 (J., - tu, 2, -, ,1+.2,21 .^ |. _Jy* . fo ) l _w_o

1 ' - - t r s' Lt

{'t2 al A,e s/P"*l th 6 ff

A = I o -l o I t^tr -e^/^"

i l+ o-+ [ e" + la t f

L e o 9 lY = A x a ^ / K y : [ " , o : j

( - o o

*|, 7U** eu arffal*-( fe

HW3

HW3

!!!!!!clear all!k=[1.5,0,0.5;0,1,0;0.5,0,1.5];!m=[1,0,2]';!x=m*ones([1,1000])+k*randn([3,1000]);!A=[0,sqrt(2)/2,1;-1,0,0;0,-sqrt(2)/2,1]';!y=A*x;!plot(y(1,:),y(3,:),'o');!title('y1 vs y3')!figure!plot(y(2,:),y(3,:),'o');!title('y2 vs y3')!figure!plot(y(1,:),y(2,:),'o');!title('y1 vs y2')!!