bài báo cáo số 9
TRANSCRIPT
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BI BO CO
I/ Ta vct trong c s cho trc.Tm ta ca mt vct trong c s cho trc.
1. C s l thuyt.
a) Cc lnh trong matlab.
Size (A) : kch c ca ma trn A.
Rank (A) : hng ca ma trn A.
Det (A) : nh thc ma trn vung A.
b) C s l thuyt.
C s E={ e1, e2, , en} l c s sp th t ca K trn khng gian vct.
Vi mi x thuc V x l t hp tuyn tnh ca E
x=e1 x1 + e2 x2 + + enxn
B n s (x1, x2, , xn) gi l ta ca vct x trong c s E.
Do , vi vct V cho trc ta c th tm c to trong c s E bng cch:to ma trn m rng [A V], dng cc php bin i s cp i vi hng xcnh rank([A V]).
Nu rank ([A V]) khc rank (A) th h phng trnh tuyn tnh v nghim khngxc nh c ta .
Nu rank ([A V]) = rank (A) th h phng trnh tuyn tnh c nghim:+ rank (A) bng s hng ca ma trn A th h c nghim duy nht v ta Vc xc nh l (A-1)V.
+ rank (A) nh hn s hng ca ma trn A th h c v s nghim.
Nhm sinh vin th c hi n:
I H C QU C GIA THNH PH H CH MINH
TR NG I H C BCH KHOA TP.H CH MINH
KHOA KHOA H C NG D NG
B MN TON NG D NG
--------*-------
BO CO BI T P L N
TI S :_9____
GVHD: Nguy n Ki u Dung
Khoa:Khoa h c ng d ng
L p : KU1201
Nhm: S 9
Tp. HCM, thng__n m___
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Tn sinh
vin
M s
L Thnh Nhn K1202515
L Th Cm Vn K1204472inh Th Ngc nh K1200136
Nguyn Th KiuLoan
K1201937
Trnh Vn H K1200928
L Dng Tun K1204271
Chu Gia Ngn K1202316L Quang Nhin K1202598
L Trn Hong Tho K1203446
Nguyn V thch K1203481
L Hunh VitKhnh
K1201623
BI BO CO
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I/ Ta vct trong c s cho trc.
Tm ta ca mt vct trong c s cho trc.
1. C s l thuyt.
a) Cc lnh trong matlab.
Size (A) : kch c ca ma trn A.
Rank (A) : hng ca ma trn A.
Det (A) : nh thc ma trn vung A.
b) C s l thuyt.
C s E={ e1, e2, , en} l c s sp th t ca K trn khng gian vct.
Vi mi x thuc V x l t hp tuyn tnh ca E
x=e1 x1 + e2 x2 + + enxn
B n s (x1, x2, , xn) gi l ta ca vct x trong c s E.
Do , vi vct V cho trc ta c th tm c to trong c s E bng cch:to ma trn m rng [A V], dng cc php bin i s cp i vi hng xc
nh rank([A V]).
Nu rank ([A V]) khc rank (A) th h phng trnh tuyn tnh v nghim khngxc nh c ta .
Nu rank ([A V]) = rank (A) th h phng trnh tuyn tnh c nghim:
+ rank (A) bng s hng ca ma trn A th h c nghim duy nht v ta Vc xc nh l (A-1)V.
+ rank (A) nh hn s hng ca ma trn A th h c v s nghim.
2. Code chng trnh.
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function toadovecto
clc;
A=input('Nhap ma tran co so A= ');
[mA,nA]=size(A);
V=input('Nhap vecto V= '); %nhap theo hang
[mV,nV]=size(V);
while mV>3 || mA~=mV
disp('Khong phu hop. ');
A=input('Nhap ma tran co so A= ');
V=input('Nhap vecto V= ');
end
if rank(A)~=rank([A V])
disp('He vo nghiem -> khong tim duoc toa do.')elseif rank(A)==rank([A V]) && rank(A)==mA
disp('He co mot nghiem duy nhat.')
toado=nghichdao(A)*V
elseif rank(A)==rank([A V]) && rank(A)
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if m~=n
disp('ma tran khong vuong')
else
d=det(A);
if d == 0
disp('ma tran suy bien')
else
for i=1:m
for j=1:n
B=A;
B(:,j)=[];
B(i,:)=[];
C(i,j)=((-1)^(i+j))*det(B);
endend
C=C';
X=C/d;
end
end
end
3. V d c th.
Ma trn A=
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V=
Ta = [-1.4167;-0.5833;2.9167]
II/ nh ca mt vct cho trc.
Cho nh x tuyn tnh f bit ma trn ca f trong c s E l A. Tm nh ca mtvcto cho trc.
1. C s l thuyt.
a) Cc lnh trong matlab.
Size (A) : kch c ca ma trn A.
Rank (A) : hng ca ma trn A.
Det (A) : nh thc ma trn vung A.
A\B : X = A\B A*X = B.
b) C s l thuyt.
nh ca nh x tuyn tnh f : V => W
nh ca nh x tuyn tnh f l tp hp tt c cc phn t y ca khng gian vecto Wsao cho tn ti x thuc V y = f(x)
Imf ={y W | x V: y = f(x)}
Nhp vo 1 c s E ; ma trn ca f trong c s E cho trc,v 1 vecto cn tmnh ca n.
Bc 1: tm ta ca vecto trong c s E.
Bc 2: ta ca f trongnhn A v ta va tm.
Bc 3: kt qu va tm nhn ln lt cho tng vecto trong c s E.
Gii thut da trn cng thc sau: [f(x)]/E = A/(E,E). [x]/E.
2. Code chng trnh.
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function baitap2axtt
E=input('nhap ma tran co so E= ');% nhap ma tran co so m = n
[m,n]=size(E);
while rank(E)~=n || m~=n % xet dieu kien cua ma tran co so
disp('E khong phai la co so ,hay nhap lai')
E=input('nhap lai ma tran co so E= ');
[m,n]=size(E);
end
A=input('nhap ma tran tuyen tinh A trong cs E = ' );
[mA,nA] = size(A);
while size(E)~=size(A)% yeu cau co cua A va E phai bang nhau
disp('A khong phai la ma tran tuyen tinh trong co so E, hay nhap
lai')
A=input('nhap lai ma tran tuyen tinh A=');
end
V=input('nhap ma tran theo hang V= '); %nhap toa do vecto cho
truoc theo hang
[mV,nV]=size(V);
while mV >3 || mA~=mV
disp('Khong phu hop. ');V=input('Nhap vecto V= ');
disp('toa do vecto V la :')
disp((V)')
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end
if rank(E)~=rank([E V])
disp('he vo nghiem,khong tim duoc toa do cua V trong E.')
return
end % moi nguoi doc ky doan code nhe,cho nay hoi kho hieu xi.
if rank(E)==n
x = E\V
P = A*x
for i = 1:mA
fx = P(i)*E(i,:);
end
disp('anh cua vecto cho truoc la:')
disp(fx)
else
disp('he EX=V vo so nghiem')
disp('he vo so nghiem, co so khong gian nghiem cua AX=0: ')
disp(null(E)')
end
3. V d c th.
ma tran co so E= [1 2 3;3 4 8;2 0 9]
ma tran tuyen tinh A trong cs E = [1 3 4;4 5 9;1 9 8]
ma tran theo hang V= [1;3;7]
x =
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-1.0000
-0.5000
1.0000
P =
1.5000
2.5000
2.5000
anh cua vecto cho truoc la:
5.0000 0 22.5000