given A={(1,2,1),(2,4,2),(3,6,3)} find(adsbygoogle = window.adsbygoogle || []).push({}); rand invertable matrices Q and P such that Q^{-1}AP={(I_{r},0),(0,0)} where each zero denotes a matrix of zeros not necessarily the same size

paying special attension to the order of the vectors write down the bases ofRwith respect to which Q^{3}^{-1}AP represents the mappingx->Ax

i think i can do the first part getting row opps of r3-3r1 and r2-2r1 and then column opps of c2-2c1 and c3-c1 giving me {(1,0,0),(0,0,0),(0,0,0) and therefore r=1

then i do I_{3}with the same row opps giving Q^{-1}={(1,0,0),(-2,1,0),(-3,0,1)) giving Q=(Q^{-1})^{-1}= {(1,0,0),(1/2,1,0),(1/3,0,1)

same with the column opps on P gives me {1.-2.-1),(0,1,0),(0,0,1)}=P

i beleive this is right but have not done it in a while and may be messing up the method so a check wouldnt go a miss, also i dont know how to do the second part of the question, it looks slightly familia with the getting vectors in the right order but i cant remember where to start so help here would be aprichiated thanks. on a side note this is revision not homework so feal free to splurt it all out :P

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# Homework Help: Canonical matrix question

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