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Math 205B Quiz 04 page 1 02/05/2010 Name. Siete olvhens -6 -12 -17 -7 5 by m 10 8 9 T=2 be n 1. Let A= 2 0 1 -1 -1 |, b= |63|, and d= | 3]. Label the column vectors of A as ¢1, -.., ¢5- 3 3 1 5 2 by 2 —t =1 =33.-1 2 bs, 1 -6 -12 -17 -7 5{/10000 100 0 OJf0 0 1/2 1/16 3/16 10 8 9 7 -1)0 1000 010 2 41/0 0 -1/2 5/16 —1/16 FACT: 2 0 1 -1 —1]/0 0 1 0 O| hasRREF| 0 0 1 -1 -1/0 0 0 -1/8 -3/8 3 3 1 5 2;00010 000 0 Oj1 0 -3 2 —6 -l1 -1 -3 1 2;00001 000 0 Oj0 1 -1 —2 2 1A. Use the FACT to find any/all conditions on 61, ..., bs which are necessary and sufficient for b to be in the span of the column vectors A. the last two rmls J the RREF iy fhe a Lay the sft Ppreredted hy PS=be amital <> OF b, - 3b, +2b,- 6b, Is = b = b, -2b,, + 2b, 1B. Verify that cs does indeed satisfy the conditions in 1A. ai Ficch condition QD = 5 ~3(-1) + 2(2) ~6(2) 2] Send anditon © W -1-(1) -2(2) +2(2) ? = 54344712 7 = -14t -444 = (2-2 7 = O+0 = OF = 60 1C. Find all values of m and n for which d is in the span of the column vectors A. Using the conditiens trom 1A S O= m -3{3) +2(2) “tt! og {Orm- Fae O= n-3-2(2) +2) “I? . ; o=m- m= ore. n-s Finis 1D. Is cs a linear combination of the first four column vectors of A? If so, find an explicit LC; if not explain why not. one wt & dlarsile | erasith. fhe agaoted merix [8 & E &)/ 5], We competstions hectsiand beciwre ts h he het. [rate H. lcalomr fe | foes NOT chang ts keer! J So ta soldtaans 4 XG eRe enya als Me RZ |e) | ap | iI [4 if we pik xy =O (say) Hhem a/ i md Peed Le ae o Big [OE 1-1 | tas mn ene mp yy, fg acs eu ALTERWATE: Soh: — Al sols 4 Ax = ° dine gitn by the REF ake hed, Go X20 X= -Ung Xe Gwe Xe ww 1 So Hook 08, lee, +2, +08, +e =6 Aye: baths (amd ky= 0) =a 2 ~.=5 x & free * i @ soln d XG te tS te Xs 9 free in the, © ape uth @ penne weg ST sabain boas Yeates ¥,--%q , thn Ee %-% |MORE AN sWeKs (iE 8iF) neste. % in Lt ae allernat, som ha 5! (x, 9-71) New GE! Why 
