Could someone help me out with questions (a) and (c), just the first couple of steps.

Any help is appreciated! (Rofl)

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- Apr 13th 2010, 01:22 PMDarKDetermine if W is a subspace of the vector space V.
Could someone help me out with questions (a) and (c), just the first couple of steps.

Any help is appreciated! (Rofl) - Apr 13th 2010, 06:06 PMdwsmith
The axioms are scalar multiplication and vector addition, correct?

- Apr 13th 2010, 06:13 PMDarK
- Apr 13th 2010, 06:23 PMdwsmith
part c

$\displaystyle \alpha p(x)=\alpha(a+bx^2)=\alpha a + \alpha bx^2$ where $\displaystyle \alpha \in \mathbb{R}$

Therefore, $\displaystyle \alpha a + \alpha bx^2 \in V$

Do addition the same way. - Apr 13th 2010, 06:34 PMdwsmith
The key to the addition is that a and b aren't negative.

- Apr 13th 2010, 07:07 PMDarK
- Apr 13th 2010, 07:10 PMdwsmith
If k is negative, a and b are still positive.

ka=w would be negative. - Apr 13th 2010, 07:14 PMdwsmith
The reason the problem says that is so this doesn't happen:

$\displaystyle a+bx^2+a+(-bx^2)=2a \not\in V$ - Apr 13th 2010, 07:19 PMDarK
Ok, that makes alot more sense, thank you!