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Math 205A Quiz 01 page 1 January 11,2008 NAME, Supyesfod fol. 1. By hand, find a matrix in RREF which is row equivalent to the following matrix. Show and label all your steps as we’ve done in class, for example, if you add 4 copies of row 5 to row 8, write “rg — rg +415”; if you swap rows 4 and 5, write “swap ry and rs”, etc. (you don’t need the quotes) Use steps that make the work easy. & | * 1 2 2000 “ai | met fo a ee : eet | eg 10r Ll a | Yoo oR e 000 10 30 Zooe 604 a [OR oO Lt 100 50 151 2. swap 626 | 0 © $0151] G<—4-505/1 go oT wores | (2) ened spt by |g ya ale CASE 0 % in proaicn ME (fot | Cee oO Ob A 6 MOE mie. BUT Se RREF thal {6 RREF © ow aya pe ents main’s 5 it ai MaRReeT tgp an to xe/ 2. Suppose an augmented matrix is in RREF and one of its rows is 0000 1. a2 ( i BP is x= @fe) “ onght Jat be 2A: Can there be any rows below this one in that augmented matrix? Explain. peceiter yes pts poteible be 9 Sch rou Weill have re eo rairie be ail wos, 2 6 P00 code =a fr eam 2B: Does the underlying system of equations have no solutions, one, or infinitely many? Fully explain your answer. 4 J, alps , lecate DOCO! peerts Ae agention Oy, #08, Ok, Ox, = 1 5 ti Annet be cai by ding values P Sora % snee OFT, 3. Suppose the augmented matrix corresponding to some system of equations is row equivalent to 1.0 =2.-0::3 O11 500 00 o11 3A: What are the solutions? (Express them in terms of any free variables) X,2 342%, «o=5 - eae iby; easy sd 20 % tan be tote aclitacd) xy e1 3B: What are the pivot columns of this matrix? Use notation like ce, ¢2, ¢ ote. CG at Gy, (adanns vib laibly Li hh, REF) 
