# subspace of V

• March 17th 2010, 01:30 PM
ephemeral1
subspace of V
How do I verify that the following is a subspace of V?

w=(x,y,2x-3y), x and y are real numbers. V=R^3

I am stuck at how to set it up. This is what I think.

(x,y,2x-3y)+?=

• March 17th 2010, 02:59 PM
Drexel28
Quote:

Originally Posted by ephemeral1
How do I verify that the following is a subspace of V?

w=(x,y,2x-3y), x and y are real numbers. V=R^3

I am stuck at how to set it up. This is what I think.

(x,y,2x-3y)+?=

$(x,y,2x-3y)+(x',y',2x'-3y')=(x+x',y+y',2(x+x')-3(y+y'))$
• March 17th 2010, 03:10 PM
Raoh
you don't have to verify each axiom,
$w=\left \{ x(1,0,2)+y(0,1,-3)\mid x,y\in \mathbb{R} \right \}$
$=\texttt{Span}((1,0,2),(0,1,-3))$