Show that two polynomials cannot span P2.

[kingkong69]

Hi
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?
Thanks

 

[DonAntonio]

Hi
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?
Thanks

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 ax^2+bx+c\,\,,\,\,a'x^2+b'x+c'\,\, , with a,b,c,a',b',c' elements of the field, and show that

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

DonAntonio

 

[kingkong69]

Hi
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

 

[DonAntonio]

Hi
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'm guessing you actually mean that you have to find a basis for the space generated by that given set of vectors...right? ***


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


*** Once again, I'm guessing you mean you write every polynomial as a row or column vector (it never matters, believe me) and then you

form a matrix with those rows (vectors) and then you reduce it...right? ***


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

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

DonAntonio