Question

LetA= [aij]n×nandB= [bij]n×n, and letC={v1v1v1,v2v2v2,...,vnvnvn}⊂Rnbe a basis forRn. Assume thatAvkvkvk=Bvkvkvkfor all1≤k≤n. Show that(a)Aekekek=Bekekekfor all1≤k≤nwhereE={e1e1e1,e2e2e2,...,enenen} ⊂Rnis thestandard...

LetA= [aij]n×nandB= [bij]n×n, and letC={v1v1v1,v2v2v2,...,vnvnvn}⊂Rnbe a basis forRn. Assume thatAvkvkvk=Bvkvkvkfor all1≤k≤n. Show that(a)Aekekek=Bekekekfor all1≤k≤nwhereE={e1e1e1,e2e2e2,...,enenen} ⊂Rnis thestandard basisforRn.(b)Axxx=Bxxxfor allxxxPRn.(c) Find Null(A−B).

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