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Math 205A Quiz 03 pagel January 25,2008 NAME SU. ted WU soltions 7 12 2 -l17 37 1. Let A= ae oa ee ,lte= a0 and let vj, v2, v3, and vq be the corresponding 2b 3 0 13 3 2 4 -!1 19 columns of A. LA: Write all the solutions of Ax = ¢ in the form p+ v), where p is a particular solution of Ax = ¢ and v;, represents all solutions of the corresponding homogeneous equation. Write down any RREF matrix you used to help solve this problem. By calculate, the RREF ft [al é] bh fo PS af] shay the lites Kiet dy mPa) yall oS X, 2-1 + x, +2x, x J I oo 0 ®le > 3 gle 2 Fe sla f th fexp | let)? 0 6 6 Olga f Ax zs ¢ x; = x; as x, 0 ' 0 %y (free, 4s 4 Xq 0 0 ! 1B: Find another particular solution and explain how you got it. Lane a ) olas d At=2, @ ta e ang choices: f Xy 3 xq aane gue (att) ns aE , & far cramps Ou fhe %=/| Pxy=l bel Re a af} «ff ‘| f* gle by atm "2 Ou x= ¢ 3 2 : ” b; 1C: Let b = bs be any arbitrary vector in R*. What conditions (if any) must b,, bo, by and by satisfy ale. by isin in order for b to be in the span of v;, vz, v3, and v4? Use the method discussed in class, and again, write mor, down any RREF matrix you used to help solve this problem. 2 = f - (oe re askin ; hen apes KU 4X4 Ke xy 2b fave « whe ie abiansed how He underlying system d egnt can le represented vin “sper -detmen bed marie x (ym Hy hk Wh) i aa Rew (2 2 -l¥ ll 0 oe . f ze a -q4 -l @h)fo tee hk ededstor ola elo e@+2 i 3 e o ef @ . “AREF 0 O @ @ fo wc 3 2 4 tlecet has eo 0 0 Flora is tby-by ing system thet | ao he rh Gy “90 ag, Loti) © OAM Sy O= 6, -17b, tb, 1D: Verify that the entries of ¢ do indeed satisfy these conditions; show your work tf O = 37 +2013 -1F-19 = 27 4286-3223 =O oF “26 -0P IR 4 BG 2G -221 4247 2 OW pan{Vi, Vz, Vy, Va}? Explain your answer. 5] ces wt cil bate Conditions vil wh be a &, + . : hh of PPS vie, B wall nd bein 8) ae Gobir f 5% 95 2% 518 ale" Mew 1E: Does R4 = NO, sine f B= 
