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Show that two polynomials cannot span P2.

  1. Apr 23, 2012 #1
    I know the dimension is 3, two polynomials has dimension 2 only so it cannot span P2.
    How would I go about showing it if I were to write it down mathematically?
  2. jcsd
  3. Apr 23, 2012 #2

    Do you mean P2 is the space of all polynomials (over some field, say) of degree less than or equal to 2?

    Well, take two such pol's [itex]ax^2+bx+c\,\,,\,\,a'x^2+b'x+c'\,\,[/itex] , with a,b,c,a',b',c' elements of the field, and show that

    [itex]\alpha(ax^2+bx+c)+\beta(a'x^2+b'x+c')\,\,,\,\, \alpha \,,\,\beta \,\,[/itex] in the field, cannot possibly give all the elements of [itex]P_2[/itex]...

  4. Apr 24, 2012 #3
    thanks i get u.

    i have a question for you.
    when I am given a set of vectors, i am asked to find a basis for it.

    I solve it to Reduced row echolon form and get the basis.

    But sometimes i have to write the vectors in columns, sometimes in rows for the matrice.
    Sorry for being unclear

    Do i need to check if the vectors are linearly independent in column space form? and then apply it in row space if they are dependent?

    Thanks DonAntonio
  5. Apr 24, 2012 #4

    It doesn't matter rows or columns: it'sjust the same at the end.

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