Ciu nio sau diy li mfnh d£ dtin'g: a L li khong gian Yecto con cua R1.. Tim m£nh di sal trong cic phat bilu sau: hang cua h£ vec to khdng thay d... Tim m6nh.de dung trong cac phat bilu s
Trang 1X K H 6 N G G IA N V E C T O
1
Chs A !a ma tran cap 2 c6 dinh thtic bSng 0 Cau nao sau day la mfnh d l dung:
a) A la ma trSn khong b) hal dong cua A doc l&p tiiyen imh
t Hai dong cua A ty If d) Cac phircmg & Iren dlu sal
2
Trong kh6ng gian vectoR^cho clcvec ttf
XL=(2,Sr 4,2), XJ = (-3,2,-2,1), X,= (5/2A7), X ^ & S ^ m 3- !)
V6i gia tr| nao cua m thl X„ Xy X * X la m&t ccf sb cua bh6ng gian R<?
3
Cac tap sau day tap nao la kh6ng gian vgc ta con cua khfing gian R 3 :
a Y ,= x+y) :x,y en ) b) V2 = ( ( x + 1, x , y ) : x ,y e R } c) Y3 = { ( jc ,y ,- l) :x ,y e i!} d jV4s { ( - x x x + l ) :* e i c }
4
Cho cac vectcf a, b, c doc lap'tuyen tfnh CSu nko sau day la mot menh de sai: a) r{a, b, c} = 3 b) r{a, b, c, a+2bi-3.c}=3
c) r{a, b, a+b+c}= 3 a) Cac cau tren deu la menh de sai
5
Cac tip sau day'tap nao la khong gian vec ta con cua kh&ng gian R 3:
aj Vj = {(x,y, x - y) : x,y e 4 b) V2 = {(2;x,y): x ,y e R}
c) V j = \ x,y,x+ y^ \ ):x,yeR ) d )V ,= {( x ,2 x ,x + l) :x e Jt}
6 Cho y = x ^ x ^ R j Kh6ng gian vfc tor con V co so chlla la:
7. a) (-7,5,-2) Toa do cua vecto (4, -3,2) theo co sa {(1,1,1), (1,1,0), (1 ,0 ,0 )} cua R 3 la b) (-5,7,2) ' {-5,2,1) d )(5 ,-2 ,-7 )
O
Tap nao trong cac tap sau day kh6ng ft kfiong gian con cua R3
a) E = {(x, 0 ,0)|x e R} b) F = {(x, 0, y) e R3}
t)G = {( x ,ls2) e R 3}' d) H = {(x, y, z) e R3| z = x + y}
9
Khlng dinh nao trong cac khing diah dudi day la sai
a) Moi hi vecto trong Ra co nhieu.bcm n phan t i dlu phu tbuoc tuyentirih
b) Moi hi gom ra vecto doc lap tuyen ttnh trong R"(m las6 nguyen dnang va m < n) deu
co the bo sung n S tn vec to trong R° de dupe irt6t ccf sd cua R°
cj Moi he vecto trong R° co so phon tfi nho hem n deu doc lap tuyen tinh
d) Moi he goni n vecto d6c lap tuyen tinh deu la co sd cua Rn
Cho a=(2, - 1 ,1); b=(■ 1 , 1 ,2 ) ; c=(-2,1 ,0 ) ; khong gian vec tor smh ben he vec tor
a, b , c, 2a-c Cosochieu Ia: a )l: b) 2; c)3 d )G iatrjk h ac
H
rim menh de dung trong cac pbat bieu jaur hang cua he vec ta thay doi neu;
a Nhan mot vec to cua he yoi 1 so thuc k)z)6i vi tri 2 vec to trong he cho nhau
c)Nhanlvec ta cua he vd! mot so k ^ c kh6ng c 3oag 2 v6c ter trong he vtf nhau
n ;
i
Tim menh da sai khi noi rang hang cua he vie ta khong thay doi neu:
a) Nhan mot vec to cua hi voi 1 so tbuc
b) Them vho hay bet ai 1 yectcf bieu tfci tuyen tjnh qua cac vectc; cdn la!
fl'Them v?.o he Yscto khong
<
l3 Cho he phuoTig frlnh: A.sraX K, = (0)^,,, co nghiem duy nh^t Khi d6 hang ma :ran A :
Dai hoc Ngoai Thuang
CuuDuongThanCong.com https://fb.com/tailieudientucntt
Trang 2a) Nhdhon m M Nh5 {ion n c) Bing m i Bing n
14 a Pj, Pj, Ps li co sof c ia R3 Cho P^d^O ), P ^ C W ), P3=(0,1,1), X=(l,5,2) Khang djnh n&o sau dung: b) r(Pv Pv P J * 2
c) Pu P*, Pj, X ddc lip tayen tfoh d)Cac th ing dinh trta dlu sal.
15.
Cho tap L={X=(x„ 13Cj = 0> Ciu nio sau diy li mfnh d£ dtin'g:
a) L li khong gian Yecto con cua R1.
$) L khdng phi! l i khdng gian r©?tc con cua R\.
c) L khdng glan yectcr con cua R? co chilu bslng 2.
d) L li khdng glan recto con cfia R1 cd co «5r }i (1,1).
16.
Cho t|p L=£X=(xJ, Xj) | Xj = a x1 + b} Ciu nio sail diy li m^nh dl ddng: a) L li khdng glan recto con cua R\
M L khdng phi} li khdng glan recto con cua R\
K L li khdng gian recto con cfia R3 n£u b=0.
d) Cic cin tr£n dlu li mfnh dl sal.
17.
Trong khdng glan recto R4 cho cic recto
X1=C?,5,-4,2),- X j = (-3,2,-2,1), X3 = (5>:2A7), X4=(2^,-4,3m2-l) Vdi gla tn nio o5a tzi thi Xlf Aw X37 X4 li mot co scr cua khdng gian Rs?
a) -1 b) 1 r a ^ i l d) Phuong in kh£c 18.
Cho h* recto a^U A -1,1); a3=(0,1,2,1); a3=(l,1,1,1); a4= ( 2 ^ n ) Vdfigia tr| nio cua rp thl a, bleu diin tuyfn tfnh qn^ au a3?
a) m -2 b) m= -2 c) V m d) m l i mdt gii tr} khic phircmg in trSn.
19.
Cho cic recto a, b, cddc lap tuyen tfnh, r i x=a-b, y=b-c, z=a+c Ciu n*o sau day li mdt tnenh dl dung:
a B l $ recto {x, y, z} ddc lip tuyen tfnh b)H£ recto {x, y, z} phu thudc tuyen ttnh c)H& yecto {x, y, x-y} ddc lip tuyen tmh, d)Cac ciu tren diu li m£nh de sal 20.
Tim m£nh di sal trong cic phat bilu sau: hang cua h£ vec to khdng thay d<3i nlu:
a) Cdng 2 rec to trong hf roi nhan b) f)6i ri trf 2 rec to trong hi cho nhau c) fjhin 1 rec to cua he rdi mdt so khac khdng: ^ Ca 3 trie ah d 4 tren dlu sal.
21.
Cho h€ recto {X„ X*, X J ddc l|p tuy£n tfnh {Xu Xv Xv X J phn thu$c tuy^n
tinh Ciu nio sau li menh dl dung:
z) { Xv Xj} phu thudc tuy^n Hnh.
b) He con bat kl cua {XJ5 Xv X3, X J deo phu thudc tuyen tfnh.
c) Moi h& ch6a { Xv X J deu d^c l&p triyen tfnh.
<j X« l i t 6 hop tuy£n tfnh cua C^pX^XJ
-22.
Cho hf m recto n chl£u'S={Xv Xj, X„ } ddc lip tuyen ttnh.
Ciu nio sau diy li raenh dl dung:
a) Bot dl mdt recto cua hi S thl h4 khdng c5n ddc lip tuyen tfnh nfra.
b) Hf { X u Xj, X „ , X j+XJ ddc lip tuy^n tfnh.
c) Them rio mdi recto cua h§ S thinh phin thtr n+1 thl hi r in d^c lip tuyfn tfnh.
d) r{ Xj, X-o X„}< r { Xt, X-2, ^ X„,, X ^ X J,
23,
Trong khdpg gian RJ cho x = (7, -2, J.), ax = (2,3,5), = (3 ,7 ,8)
83= (Ij^ l^ Y d ig ia trln a o c u a 2 cho d ad id iy ta x lit^ h o p toyen tfnh coaa1} 24, a^:
a> ^ = !2 b) X, = 13 £ \ ^ 15 / d ) = r -12
24.
Kf 3
phu thu?c tuyen tlnh trong R3 khi a) X = 1 h) X= c) X = -1 d) X * 1
Trang 3a) { Xj, X j} d6c’lap tuyen tfnh
e) { X„ X,} phu thuftc fnygn tinh
b)r{X 1,Xil} = 2.
d)r{ X „X 3} > 2 ,
Ma tran A =
kha nghlch khi
a)m = 5 b) ra 5*5 c) Vm d) khong com Cho A, B, C la cac ma tran cap m x n tuf y Khang djnh nao sau diy la dting
c) (A + B)C = A.C + B.C -t (A + B) + C = A-f (B + C) _ L Cho ba ma tran vu6ng cap n: A = (a-),*,,, B = C = (c5)„Xll)
X e R Tmh ch£t nao trong cac tfnh chat sau la sai a)_ (AB)C = A(BC) b) A(B -f C) = AC-i AB
Chon phuong an nao de c6 menh dl sai:
Hang cua he vec ta cothe thay doi neii
a) nhSn ih6t vie tor cua he vdi s$ thuc fc 0oi t| tri 2 vec to trong he cho nhau c) them Yao 1 veccola.fo hop tuygn tmh ciia cac vecttf cua he
d) lgy m6t vector nh&n v6i mot so r6i c6ng Yao recta khac trong he. _
Cho A la ma tran yuCng cap n Tim m6nh.de dung trong cac phat bilu sau* a) Hang ma trin A bang hang ma tran kA voi k la so thuc tuy y b) Hang ma tf-an A kh5c hang ma tr§n kA y6i k 5a s6 thuc khac khfing
c) det kA = k det A vfii k la so thuc tuy y
tf det kA = k" det A yoi k la so thuc tuy y. _
6
- 1 2 1 - 1 1
a -1 1 -1 - 1
1 a 0, 1 1
I 2 2 -1 1 b) a = 0 c) khong t$n tai a d vdl moi a
Yoi gia tri nao cua a thi hang cua ma tran
a) a * 1
bang 4?
Tim phuong an dung trcng menh de sau: hang cua ma traa
1 m —1 2
1 - 1 / 7 ! 1
2 - 1 1 - 1
3at gia
tri nho nhat khi m bang:
Cho^ =
2 -1 3 B = lU 1 0
- 8 2 -9
5 0 3
5 -1 5
b)X=
Tim X bill AX = B
8 - 2 9 l
5 0 -3
5 -1 - 5 j
Dai hoc Ngoai Thirang
CuuDuongThanCong.com https://fb.com/tailieudientucntt
Trang 4c )X
- 5 0 3
- 5 - 1 5
d)phucmg an khac
Hm a dl hang cfia ma trim
a) a = 0 _b) <r = l
3 1 4 1
3 - 1 1 0
3 3 7 2_
c) g = -.l
li nh& nh£t?
d) phnong An kh ic
10 Vdi gi& trj n io cfia a thl haiig cua ma trin
a) a = 0 b) a g 1
b in g 2 ?
I 10 17 4
c) a = -1 _d) v6i moi a
Cho A = I 2 - 2 m + 5 m 2 + l
a, m * 2 v i m * - 1 b ) m * - 2 c)m = 3 d) k£t qua khac.
12.
Cho da thurc f(x) = x1 B 5x + 3 vi A = '* j KhJ 36 f(A) bang
13.
Phucmg trinh ma trim
a )X =
3 2 -4 X = 10 2 7
co nghiem la
14
15
Khiog djnli nio sau diy dting:
1 X 0 0
C h o m a trin A = 1 1 X 2
1 1 2 X i8r(A )=3 ngaX * 2 b) r(A) < 3 neu X = 3.
7(A) - ? 7 $ i w ^ H e pVin?Tifi A t ? «j? nV.o <j4u sal
Cho X :
* a - Cau n io sau d aj la menh de sai:
a) X ,-(a+d)X+(ad-bc)E=9 c) d a(X )=0 thl X*=(a+d)X
bj Xl=8 thl X=8.
d ) € g g £ M a g d f g h # 5 6ho S iu sa l.
Cho 2 ma tr in yu&ng cung cap A vi B, menh de nio sau diy sai:
Trang 5c) TSn tai long A+B d Co dang thtic: (A+B)2 = A2+2 AB+B2
17
Cho A 1& ma tran Yu6ng cap 4 c6 hang bing 2, khi do hang ma tran phu fa^fp cua
A co hang bang:
18
Cho A 14 ma trln vu ong cap n ya A2 =' E (E la ma trari dcm 7} cap n)
Tim menh de dung trong cic mlnh de sau:
a) A = E-t b) Hang ma tran (A-E).(A+E) bang n c) A = - E d) Hang ma tran((A-E)-f-(A+E)) b£ng n
19
Cho A !& d a tran yuong dfp n, det A * 0 Khi do hsmg ma tran nghich dio cua
ma tr&n A2 co hang:
20
Cho 2 ma tran yuong cilng cap A va B, menh de nao sau day sai:
a) Ton tai hleu A-B b) Ton tai tich BA c) Ton tai tong A+B d AS BBA= (0)nxn
3 DINHTHtfc
1
Cho A, B la hai ma tran yuong cilng cap n tu} y Khang dinh nao duoi day la dung trong d on > 2 ) :
a 'det(AB) = det(A) detfB) b) det(AB) > det(A) det(B)
c) det(AB) < det(A) det(B) d) Ca 3 khang dinh tren deii sai
2
Cho A e M 3 ,| A |= 3 Hoi co the ding phep bien doi so cap nk> sau day aua A ye ma j tran B co detB = 0
a) cac cau kia sai b) nhan 1 hang cua A Yci 1 stf khac 0
c) cong 1 hang cua A yen hang khac da dirge nhan yoi 1 so
d) S 6i ch6 2 hang nao do cua A
3
Cho A «= M 5(R ] biet r(A)=3 Khing djnh nao sau day la dung?
4.
Cho A; B ia cac ma tran yuong cap nxn ( n>2) Khang djnh nao sau day la dung: a) det(A - B) = det(A> det{B); b) det(A-B) > det(A)- det(B) c)det(A-B) < det(A)- det(B); A cac kei qua khac
S.
Cho A, B la cac ma tran vudng cap n Khang djnh nao sau day la mlnh de dung: a) det(kA) = k det(A): k € R
b) det[ (x + y) A ] = xdet(A) + y det(A)j x, y e R c) det(xA + yB) = xdet (A) + ydet(B); x, y € R
c det(kAB)= k" det(A) det(B); k 6 R
6
Phucrag trinh
1 x x* x3
1 2 4 8
1 3 9 27
1 4 16 64
= 0
5
Dai hoc Ngoai Thirang
CuuDuongThanCong.com https://fb.com/tailieudientucntt
Trang 6cd'cdc nghfem 1£ a) 3,4 b) 2 ,3 ,4 ,5 I M i d) 1 ,2 ,3 ,4
Cho A; 8 Ik c ic ma trin Yu6ng dip ran ( n> 2) Khang dinh nko sau day lk dung: a) det(A-B) = det(A> det(B); b) det(A-B) £ det(A)- det(B ) c) det(A-B) £ det(A)- det(B), d Ci 3 kfalng djnh trtn li sal Cho M a trSa ruftng A =[a„ ] ^ j k la so thyc bit k|; Ma tr&n Ax =[ka, J HS.y 6m m£nh dl ddng:
a) dct At = det A b) det At = k" defc A
c) det A, = kdet A d) det A, * det A Cho ma tr^n vuflng A =[a(J ; ma ttin A, j HSy Qm m$nh dl dung:
a) det Ax = det A det (A + 2AJ = (-1)“ det A c) det A) — -det A rii 3 phirtrng in tr£n dlu 1£ sal
10.
11.
M;nh d l nio dung:
a) D|iih thtic d p 6 c6 tich die ph&n tu him trSn du&ng chSo chfnh mang aau +
b) Djnh thtic dtp 6 c6 tfch die ph&n tu aim trio dufmg ch€o chfnh mang d£u -c) B|nh thtfc dip 6 c6 tfch cic phin tur nim trio, dirbng ch€o phu mang diu -+■
d) Cdc m&nh dl trtp dlu sal, _ M&nh d l nio dung:
a) £Hnh thfic dfp 6 cd tfch cic phin tu nlm tren dudng ch€o chinh mang d[iu
b) Djnh thdc cap 6 cd tich cic phan tu nlm irka ducftsg cfc^o phu mang d lu ^
c) t>juh thdsc cap 6 co tfch cac phin tir nlm tren dtfimg ch£o phu mang d&i d) Cac menh d l tren dlu sa3 _
12
ChoB
C =
■r. Tim ma trSn C thoi man: 3B 6 2(B + C) = 2 E , duoc
d) phuomg in khic
"-1 3 "1 -3 z l i f
2 2 b) C = 2 2 c)C = 2 2
2 2 2 2 2 2
Cho ma tran yu£ng c£p 2 co cac phin tdUt2 hoic »2.HSy loal tril 3 ket qu i sai dl cdn 1
ket qul dung:
a) flet(3A)=-72 _ b) det(3A)=41 vc) det(3A)=18 d) det(3A)=27 13.
14.
Giaipt: 1 a a a
1 b b2 b3 = 0
1 c c i
B ilt a,b,c la 3 sS thac khic nhau timg do* m$t a; pnuong trinh TO nghiem t Pnucmg trrnh co 3 nghJfm a,b,c
l riiPnizatiz irinh co '5 Cffniem (r'jiili cO I hghi$i&.
15 Gial pt:
2 1 - 1 3
1 2 2x x
Trang 7- 7 a)x=0pe=l b) x=0,x=-2 c>S=0;— d ) x '= 0 ,^ - 2
16. Cho
a) a=
1 x2 x 3
1 1 - 1 23b=2
= 0 Tim a,b biet.pt trfen co > 4 nghiem thuc
b) a=-2,b=-2 c) a=l,b=-2 <3, a=23b=*2
17
Cho A eM 3xS[R])B eM Jx5[R] bietdet(B) * 0 var(A)=3
Khang djnh nao sau day diing:
18
Cho A3B la ma tran'kha nghich cap 3, PA la ma tran phu hap cua A.KhIng djnh nao sai?
a) P ^ khanghjcfy b) r f P ^ ) ^ J
19
Cho A ; B la c£c ma tran Yuong cap n (b> 2) Khlng dinh nao sau day Ik menh de diing:
a) det(AB) = kdet(A)det(B); b' (A- B)1 = A1 - 2AB + B1
c) det(AB) = det(A) + det(B); d Ca 3 khang dinh tren deu sai
20
Cho ma tran vufing A cap n (n la s6 nguyen diromg), A’ la ma tran phu hop cua A Gia sur det(A) = D* khi do det(A5 b k g
21
Cho A ; B la cac ma trin yu6ng cap nxn (n £ 2 ) Khang dinh nao sau day la sai: a3 dei(AB) = det(A).det(B); b) det(kAB) = kB det(A).det(T? )
vj det(kAB) = k det(A)detfB); d) dei(kAB) = det(kA) det(B)
2"?
Cho A, B la hai ma tran Yuong ciing cap n tuy y Khlng djnh' nao duoi day la dung trong do n ^ :2 )
a) det(A - B ) = d e t(A )-d et(B ) b) det(A - B ) > det( A ) - det(B)
c) d et(A - B ) < det(A) - d et(B ) 0 Ca 3 ikhang dinh erea deii sai
23
Tim so nghiem pfcai
1 X -1 -1
1 X2 -1 -1
= 0 : a) k=l ty k=2 c) k=3 d) k=4
24
A la ma tran yuong cap c, det(A) = 1 Co the dang phep bien doi so cap nao sau day dua
A yi ma tran B co det(B) = 0:
a)Nhan 1 dong Yd? ntft so khac 0 bVBoi ch5 2 dbng cua A c)Nhan 1 dong yoi 1 so tuy y, r6i cong vao dong khac d] bnlng djnh a3 b, c deu sai
25
Cho A la ma tran vuong cap n le thoa mSn AT= - A Dinh jthu'c cua A bang (AT la ma trss
chuyen v| cua A):
a) 1/2 fc) (•I)-1 c) 0 d )!? m6t gia tr} kh? c 3 phuang an da cho.
Dai hoc Ngoai Thmyng
CuuDuongThanCong.com https://fb.com/tailieudientucntt
Trang 826. Gia trj Idn nh£t cfia djnh thfic cap 3 mi c£c phin fcuc chi nhiis gia trf 0 ya 114
a) 2 b) 4 c) 6 d) c£c phuang in da cho d£u sal.
27.
Cho djnh thtic cap 3 mi cac phan tur chi nhin gi£ tri -1 v4 1 C4u n4d sau 14 menh dl dfing:
a) Djnh thtfc chia h£t cho 4.
b) D|nh thfrc khOng chia het cho 2.
c) JE)|nh thtic chia h€t cho 3.
d) Dinh thtirc chia hft cho 6.
28 Bill |A| = fk.A] vi5i moi ma tr&n vudng A dip 2n+l Gii trj n4o n4o cfia k sau day 14 dung a) k = 0 b)k = - l c)k = l d) k 14 m6t gli tri khic.
Ci
i
Cho hal ma trin A =
AX = B co nghifm.
’a) k =* 4 b) k = ^
j 4 J y 4 B = _ 3 ^ q2 Gia tr| k nio thl phucmg trinh
4 A1 Oj [ - 3 I 3
1 c) k = 2^ d) khdng t6n tai k.
2
Cho h£ phuong trinh:
He co v6 stf nghi^mne
a) -2 bj -lh
*i + xi + *} ~ 1 2x, + x2 f 3ij = 2 3jCj + 2xj + 4x3 = 3<r
u a bang:
3.
Cho hfe 3 phuong trinh tuyen tmh hai an Ciu nio sau diy 14 menh didting:
a) Hfe da cho c6nghiem.
b) Hang ma trin hi so< hang ma trin bd sung,
cj H£ da cho v6
nghlini-d) Neu he da cho co nghiem thl djnh thdrc ma trin h6sung bang 0.
4.
f5 x + 3y + 6 z + 7 t = - l
He phucmg trinh j —2 x — 6y + (m ljz + 4t = 4 c6 nghiem duy nhat khi m
4x + 1 2 y + (3 + m 2)z + m t = m - 3 thoi man
a) m = 1 b) m = 31 c) y<5i m gi rn d) kh6ng co gia trj nao
•7
-Cho hS phucmg trinh tuyen tfnh thuin nhit g6m m phuong trinh va n AX = 0 , trong
do A = (a -) Khang dinh nio trong cac khing djrth sau r i he da dfo 14
a) T f haptn jS z iiuh c i c LCi k j x.Lu h i v£u5' iiiflv* * >*« <J«.
bj He aa cho luon luon co nghiem
c) S<f chleu cua khSns gian nghiem cua he la m - r, trong do r 14 hang cua ma tran cac he stf cua h$ da cho
Trang 96
fkx -3y + z = 0
He j2 x + y + z = 0 co nghiem khong tam thuong bhi k hang
(3x + 2 y -2 z = 0
7
" i l l " -1 0 0 Cho hai ma tran A = j 4 0 va B = _3 4 0 Gia trj k nao thl phuong trinh
4 k1 0 [-3 1 3J
AX = B co nghifm
8
( * , + x2 + ,* 3 = 1 Cho he phucmg trinh: \lxl + xr -t- 3r,, = 2
|3x, +■ 2x1 + 4r3 = 3a1
He Co vo'so nghiem neu a bang:
a:) -2 b) -1 c) 0 d) Cacphucmg an tren deu khong dung
9
Cho he phucmg trinh.tuyen tmh fhuan nhat n phucmg trinh, n i n co ma tran he so la A,
C&u nao sau d&y la menh de dtuig:
a) He da cho v6 nghiem b) He d5 cho co 3 nghiem,
c) He da cho co nghiem khong'tam thircmg
d) Neu he vectcf dong A deu doc lip tuyen tfnh thl he chi co 1 nghiem tam thircmg
10
Cho he phucmg trinh tuyen tmh fhiiln nhat n phucmg trinh, in i n co ma tran he so la A
Cau nao saii diy IS menh de dung:
a) Neu he Yectcr cot A deu doc lap tuyen tfnh thl he chi co 1 nghiem tam thirong b) He da cho y6 nghiem c) He da cho co 3 nghiem
d) He da cho co nghiem khong tam thuong
11
Cho A e M 56)X e M 6|1 Khlna dinh nao sau Iaondiingc
a) He A X = 0 luon co nghiem khong t|m thucmg b) He A X = 0 co nghiem duy nhat b) He A X = 0 vo nghiem d) Cac cau tren dlu sai
12 Tim X de he ■
a) A = 3
Axl +x2 + x 3 + x4 =1
x, + 'Xx, -rX + X =l
v6 so nghiem?
x1 + x2 + Xx} +xA = 1 l.3! + X2 + Xl ^*4 = -b) X = 1 c) X '=2 d) phuong £n khac
13,
Cho A 6 M 4, X = (x 1,X2,X3,X4)t)B = (1,2,-2,0)', biet A khz nghjch Khang dinh nao
sau day luon dung:
a) r(A ) = 3 b) He A.X = B co nghiem duy nhat
b) He A X = B co y o s o nghiem d) He A.X = B ?o JBghiem
14.
He nghiem cc ban cfia he phircmg trinh: Xj +2x3 + xj = 01a:
a)V1=.{a1= a 2 ,0 );a 2 = a a 2 );a 3=(U l)} b)V3= {a , = ( - 2 - 1 , 0 ) ; «2 = (1 ,0 ,1 ))/)
c) V4= k = (1 -1 ,1 );< 7j =(0,0,0)} d) Y3={a, =(1,2,3); a 2 =(4.2.1)}
15, ' ]
fx i + x 2 “ 2 x 3 =1
He phirong trinh j - >-i + 2 a , - x 3 = - 1 co nghiem duy nhat khl
|x, + x , -f mx3 ~2
Dai hoc Ngoai Thipang
CuuDuongThanCong.com https://fb.com/tailieudientucntt
Trang 10a) m # 1 b) in ^ 4 c) m —2 d ) m ^ 2
1$,
j x + 2 y + z = 1 Cac gia trj m de hfe j 2 x + 5 y + 3z f= 5 de he sau co nghiem duy nh£t
^ 3 x ^ 7 ^ + m 2z = 6
a ) m = ± 2 b) m ^ ± 2 c )m = 2 d) m = -2
17
Cho he phuong trinh: A nia-Xlixl = B ^ c o hang ma tran A bing hang ma trial b6 sung bing k vk h i c6 duj nh£t nghlfem Mlnh dl dfing lk:
a) k = m b) k = n c) k<m d) k<n
18.
He phircmg trinh thuin nhit sau
6xj - 2xj + 2x3- + 5x4 + 7xs - 0
9s, -.3X2 + 4^3 ■+ 8x4 + 9xs - 0 6xt - 2x? + 6x, + 7 x f + x ,-= 0 3x, - x? + 4x3 + 4x4 - x« = 0
HS Teeter nko trong cAc hf dutfi diy Ik hfe nghi|m ctj bin cfia h& phucmg trinh tuyen tfnh
trin:
a) {(1 ,0 , 0, - - i ) , (0 ,1 ,0 , ^ ) , (0 ,0 ,1 , ^ )>
b ) {(l?0, 0y ^ ^ ) , ( 0 , 0 , l , 3 , A )} c) {(1, 0, 0, - ^ , - ^ ) }
d) { ( i , 0 ,0, ~ ) , (0 ,1 ,0 , - A , J_ ), (o ,0 , 1 , - ^ , ^ ) }
19
Cho he thuin nhit
nghiem long qtiSt ct
a) (5a •• 9P, -3 a + 2p
c) (a + 20, -a + P, a ,
’ x + 3 y f 4 z + 3t = 0 2x + 5y + 5z + 8t = 0
Nghiem nao trong cac nghiem sau day la
4 x + 6 y - 2z +-24t = 0 * 5 -3 x -4 y + 3 z -19t = 0
ia he trfen , a , p), a , p e R b) (11a - p, -5 a - 4 0 , 7a, 70), a , p e R.
P ),a, p e R d) (2 ,1 ,1 f a ) , a f i R.
20.
Chon m£nh de sai trong.cic m€nh de sau.
a' H€ phuong trinh tuyen tfnh c6 the v6 nghiem
b) H£ phuong trinh tuy£n tfnh co thl Co nghiem duy nhat c) H4 phuong trinh tuy£n tfnh co the c6 hal nghiSzn d) H$ phuong trinh tuyen tfnh c6 th£ co y6 so nghiem
■
-Trong c ic m£nh d l sau vi hi phuong trinh tuyen tfnh thuan nhat, menh d$ nko sai:
a) Hf phucrng trinh tuyen tfnh thuin nhat ludn c6 ft nhit m 6t nghi£m.
b) H$ phuong trinh tuyfn tfnh thuin nhit co nghiem duy nh it khi qul trinh khi in kei thfic is dang tarn giic,
cj H^ phiromg trinn tuySn tfnh thuin nhat co vo so nghiem fihi qua trinh khu an ket
d) M9I b? phuong trinh tuyen tfnh thuan nhat voi s6 phuong trinh nh6 hon so an deu