Show that two polynomials cannot span P2.

1. Apr 23, 2012

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

2. Apr 23, 2012

DonAntonio

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

3. Apr 24, 2012

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

4. Apr 24, 2012

DonAntonio

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

DonAntonio