# MD term 2 - n.»—.WA(30 pts 3 Let V be the vector space...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ., n.»— .WA '(30 pts.) 3. Let V be the vector space of 3 X 3 matrices. Let A and C be two nonzero 3 X 3 matrices. Let W={BEV|AB=O} and U={BEV|AB=C} a) Show‘that W is a subspace of V. A , C) :L O b) Show that U is not a subspace of V. _ l;\ e (“u r; 1:: EU AuozﬂiC LSW’ Sc. o¢LA .9; ti. 0) Determine W when A is invertible. Let gene, “We. Llama; A'QQZO Q): ESQ: PNQAEl: AV‘020. Q‘ljog b Shee- (1) Determine the dimension of W when the rank of A is l. (D g: Kid Sf“ CC MAL 0(— ‘g R: 1' A . (3 ts c, L W! Wee-id!“ E f O O W O O O 1 S O r l“ is 7‘ 1— ‘“ 7: f KL “‘3 x g \-: 1, 7‘; ya“ 3% X} 7%, \IWEVU 93\$ .— 0\lL'vllollé'l/‘l' («X to \ but) 5 \rfeo— Aka «Slur a l" l'lﬂé Cclui‘wA l’ éiMQM) ié ,1: M E T U Department of Mathematics Basic Linear Algebra Midterm II COde : Math 260 Last Name I Acad. Year: 2008 _ Semester 1 Fall Name StUdent N0- Instructor 2 Department: Signatiire Date : 24.12.2008 Time 2 Duration 1 .90 inc 3 Questions on 3 Pages Total 100 Points Show your work! Partial credits will not be given for correct answers if they are not justiﬁed. (30 pts.) 1. Let 0 3 —3 1 —5 A: 01 ~1 0 ~2 0 1 —1 1 —1 3) Find a basis for the row space of A. O \ 4; o J}. t»; +2.? ‘0 0 O l l .hllli‘ﬂl} ' 7’ “1‘ a - e o o \ A .——"/° A (D \ -1 Q .-’L 4 I -1) i7\_‘i‘ \‘- _ Q 7 l L C} O 0 l l plaid. O O O O { Lo \ .-1_ O -11 {mocill} i3 ox LQAL] I £0!" V‘G LA.) '5?ch , b) Find a basis for the column space of A. . 3 \ r \ O E L) e. LI. i , i i I j“ ’ Q5 \Urvm specs; c) Find a basis for the solution space of the homogeneous system AX z 0. 7““: 7(3‘21)? “\ Q” 0 h _ i , ’ n. * “ ' X5 0 4 l- ‘x \ j . 0 O O r. o ' 0 0 .. t r . 0 X ‘ I Xe}, X S (lbw. ‘ j . D j l Q'I'aé- UC/‘PI l3 q Lgsl‘) gov Sﬁsci (40 pts.) 2. Let S = {111, 212,113} be a basis for a vector space V and B = {U1,U2,U3}, C : {101,102,103} be subsets of V where ul ; 01 +112 +213, 1L2 2 111 + 122, U3 2 121 and w1=111+v2, w2=vl—v2, wgz—vl—vg+vg. a) Show that B is linearly independent. mi. and?” LL :6 UL met at»): c\\s.‘+LLub« cCt L23 : O , . gimca Kym“); are, “MEGA”; {a keg; L\-\'C.L\C_b';0 I “41:0 I (go ge L‘ t u) ck, : o I :1 a: Q , Waite, duo”) IQ; we/ (HAD \\NA€P€4<\,94L— b) Show that C spans V. Let v 6 S, (rice, (L 3> Q be: 5:; ’umya 0W"— "‘ \"9: L (7 UL sec-AA the \l : cuf‘tioxfr‘t é V3?- 0 (snslekr 4” “\WJ‘QM . fW '1‘ X1. “XI 33.: 5can “A (Add? \ C\\]\ TbULiCXJ : ¥\w‘ At¥1vut+¥2>wj> g L \I Q \J 7“ ~¥1 ‘Xb ‘ in W \I x was) '»v-\J.+\v‘, °* x .1 ._ L 1-1: 7- + ‘51, \_ ’L i " ‘-‘ [A X c) Find the change of coordinate matrix PBS, from B to 5'. WC VWVL 3 9 \ 3 \A’ v e kl)‘ W4“ k \ ' ‘ r O r. i; RB R‘QA‘ F; K t g ‘33 L3) “‘3 \ O i 6 ¢ (1) Find the change of coordinate matrix P55, from S to B. .. \ C9 0 a o \ r “\$— \ 1 ‘ \ ° 6 “mfg L psi), ‘5 PE ; K L b O 1 0 41,7012. 0 i 0 ’0 \ ‘2) __ o \ "L 5% “ -\ -\ o “i e) Find 0 coordinate MC of a vector v E V if B = [ 1) Hi V A . . _ it w + ‘ \/ ‘: 0| 1—H + LED"? ‘CL \$3 ,9 in“; ¥1/ V‘L /\L3 Sugb ‘H/lci' V ’ Xxwi‘f 7’ 1’ \wai . . i -\J -U,+\I 9_o\*\=>‘*c C1 Kikivtl*¥b\4&:wl+ug/\+Cvt : )L‘ Olf‘i'VL'X "i‘ XLLVi”\!’1)*¥\$i ’ ‘1‘ R. /2'— l W V1 2 a], u+L+c ‘: mamas—x3 ‘M » a /2_ ' _ ~ I; . “*‘Q ~; XL "éu “‘13 \(‘b ' 3" CA [TA 1 ‘3: ‘ ‘~' (A i \ ' {L- \ 4 4 u o l 5 c, Jrkwn. \Jt an 642/ x“) Lokidd we ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

MD term 2 - n.»—.WA(30 pts 3 Let V be the vector space...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online