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Math 205B&C Name Exam 01 page 1 02/13/09 1. Suppose the solutions of a matrix equation Ax = b are written in the form p+ v,, where p is a particular solution of Ax = b and vj, gives all solutions of the corresponding homogeneous equation W —9 7 a 0 1 0 : Suppose b = g [P= —2) and v, = 22 | 0 | +25 |—2], where x2 and zz are free. 2009 5 0 0 0 0 iL la. How many rows does A have? @) How many columns? ©) because de selutine have 5 (sine Bo a £6 ofthe colina f AE this Ky yp Xe the Xe a Le 4 entats the wight: J He 7% cola ga 1b. Label the col of A as cj), C2, ..., Cp. Is the set S = {c1, C2, ..., cp} lanedrly independent? Explain in terms of the definition of linear independence. ; Mork wei! P iho a ‘aght unseen" ; we ae HOF firs he achul,entets of th Mt ve ty Know Has ae babel ay whi AR =O Gnee Fx ar Kee, at the tess Hoe as Wigs fo wide xe) + KG eMG +42 +45 2B be cate the a Sj toviel soln yore 2X2 OD, S i. ee ee Lo thee A Hinton Comes 19 £) 1c. Write c3 as a linear combination of the other columns, or explain why this cannot be done. LA can ae thé ance 1 & poste + tial a chi NOTE WELL: we OOMT Krew A, mes ete te ee And we WERE Mer Atkeo be ti: BUT be co =o * eee ome Tae so Bxamele =O Gnd r= ld OM a) ft tee sea ao ; heer (ALB) =| so eS ot x= ~4x, thy = PS x5 -2xe = -2 J 2 O andse suet olor 2 > 2 Ae f wget ° @00 ol] © 7e +02 + 23 +064 +1825 3 de hr & # G =k +hes (ther Antu dre possible thooh thot. dies J* 2%) 1d. Write c, as a linear combination of the other columns, oy explain why this cannot be done. Thi: canst be aore. For Syppece oMerweie. Hein { 9, Ha . os a AE eG 4 tc; + Mle fr Wine. ye gee cle age ' Lae be oe ([é 4 ise }q fed oe Sta Stage oy [i shen mater WHAT tay Gee] le i ecanels 2 : : ee Re oe bathed rot qak Rera. |, 1 ere ae a > eae a aa J e SA, Oe dh ehG + Gat (ey tte NP e rT WEE bee any Kt fa. tle BHO ee dale x Wey Xp20, 42% Ry A aad J PRB inti He weit Je, 6 rion pero, Bot i, gues fll slat f AaB » Gad mig, x, © Ays O, never “E “ tn badlihen, So Gy a MEP « bef ha ms: le. Show how to express b as a linear combination of all p columns in such a way that none of the ci weights involved are 0. Thi meads, bro & sola 4 AXE nie tex seh aX a0. Try ee eS ta R= Pel, = 2 +l ‘lf = E , hat b, o e i Ba Fe 28, 1G ose, te aot te eevght ae ©. 
