MATHEMATIC
Midterm 1 14-15 Fall.pdf

# Midterm 1 14-15 Fall.pdf - METU NCC LINEAR ALGEBRA MIDTERM...

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Unformatted text preview: METU - NCC LINEAR ALGEBRA MIDTERM EXAM 1 Code IMAT 260 Last Name: AcadYeari 2014—2015 Name 1 Semester IFALL Student # : Date : 01.11.2014 Signature : Time : 09:40 Duration 90 min 5 QUESTIONS ON 4 PAGES TOTAL 100 POINTS (1039133) Let U— — {( :1: ﬂy, 12:1: + yn— 32— — 0} C R3 Find a basis for U. Justify your answer, that 15, they are linearly independent and span the subspace U. 613(1,F§,O] JaL:(oz3/O m mg WW Minn \$0M (H 11 :;- x [4,4, 0) 4- i2. (0,3,0 :1" xii *3316 SPG’JE’E W5 '11 -: Spamlliﬁzj :>C&.,E,Qs a bag): it,” 2. ( 1 5+1 519155 ) Determine if the following sets are linearly independent. Justify your answers. (a) E ={(1,2,3,—1),(2,1,—1,1),(1,_4,—11,5)}c; R4. n ")4— HQGZOWF—v ”Anus—9:9 9* J‘ ,_ x/5 3*) -raliﬁro H) +jvk+5920 0L ()IW WW “554 (b) E 2 {290; + X5 —— Xe: Xa — 2x;J + Xe} Q HMS), where S = {a, 15,0}. Bang, R3 Om ‘50me Cog, €63 RH(S))W€J W “Mag/-0 +‘f(1,‘ﬂ,4):=O:-»> , 25M)”: ,_, ~> 9‘ ’«Qﬁ: :> ()ZJ‘:OJ 43“ B) b '3 ._j,\ bur—=0 ") n—p 7 u! “2.. ”.3 3.{25pt5) Consider the subset E m {(1,-—1,2,1),(—1,2,0,1),(m2,2,——4,—2)} g R4 of vectors. Find the subspace Span(E) spanned by E in terms of the linear equations in R4. Firs'i' noiﬂ ' -Ue./L UL? I “313. ,. ‘He’re—ﬁoﬂ' Spam (E) .3 SP6“ imam ‘ Bu} ‘AG’. +fqb: _._—- Time/£5 Span-«C E) S 5' 22g13+qxj Z+élx+£lj=é2wj Bye-‘7 hsaQM/Jﬁm Sel-Gjﬁaifk 33340:“ le+£3'2=0 T5 { (Gig) Qa+2£/ gngj &xr&5+2*1’w=0 \NLM SPWCE) TLZﬁélJ +14 X) Ei—Q—X‘an fgwj‘ 4.(25pt3) Consider the set E = {3: — 1, (a: + 1)(a: — 2)} of vectors from the space P3(R). Extend the set E up to a. basis of 733(1R) Justify your answer. ‘ Nola JCL‘A‘ (ACX-J) .tfxfov—x-‘QU: J) 49X #394 74x 74x2 Heme. gfmCE)=£®+gk +cxt; Q+g +3c=oj In Parka/vac...) 4 6}: SP5” CE); ‘H‘VL B) L304 66-0093) 3 Q 21%. {KAWW 5..»me Fur-HM) Swim we: mj cs? (IR) 15% Lx—t)(x+9(x»z),4) x33 ‘3 a bass im— C2093). 5.{10pt5) Let U1, U; be two subspaces of a vector space V. Show that U1 0 U2 is a subspace of V. What about the union U1 u U2, is it a subspace yet? M Ma eU,n/u7__ “a Qa+j¢& Q— U; W1 J L 130% Mi) “7.. M SMIOSPMS~ ...
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