# 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