On polynomial ring over R, decide about linear dependent/independence. $$(x^2+x+1,x^2+2x,x^2+2)⊂R[x]$$ In this case I dont really know how to start... I know what is linear dependent - but I cant see any vectors in it (I was missing at school last week - but I cant get any usefull hint in note of my friends ).

  • $\begingroup$ Note that $$ x^2+x+1 = \frac12(x^2+2x) + \frac12(x^2+2). $$ So the given set of vectors is linearly dependent. $\endgroup$ – Math1000 Oct 20 at 21:18

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