# Subspace of a vector space

• Dec 15th 2011, 07:22 AM
MAX09
Subspace of a vector space
hi

i solved this one, but am getting an answer different from the one given in the text book.

Let V= Vector space of real polynomials
W= set of all polynomials with degree>=6 and the zero polynomial(included)

Is W a subspace of V? My answer was no.

for the following set, u+v will not belong to W for

u= x^6 +2x^5 + 1 v= -x^6 +x^5 + 2

Here both u and v belong to W but the sum of those is a polynomial of degree less than 6.

The text book says W is a subspace of V.

Am I overlooking something?
• Dec 15th 2011, 07:46 AM
emakarov
Re: Subspace of a vector space
You are correct: W is not a subspace of V.
• Dec 15th 2011, 10:57 AM
FernandoRevilla
Re: Subspace of a vector space
Quote:

Originally Posted by MAX09
The text book says W is a subspace of V. Am I overlooking something?

Perhaps there is a typo in the text book: $\leq 6$ instead of $\geq 6$ . Or maybe the typo is in the answer. :)