# Thread: subspace of V

1. ## 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)+?=

I don't know what to add. I know that if w=(x,x1,x2), I can add that too (y,y1,y2). But what about (x,y,2x-3y)? Please help on how to set it up. Thank you

2. 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)+?=

I don't know what to add. I know that if w=(x,x1,x2), I can add that too (y,y1,y2). But what about (x,y,2x-3y)? Please help on how to set it up. Thank you
$(x,y,2x-3y)+(x',y',2x'-3y')=(x+x',y+y',2(x+x')-3(y+y'))$

3. you don't have to verify each axiom,
$w=\left \{ x(1,0,2)+y(0,1,-3)\mid x,y\in \mathbb{R} \right \}$
$=\texttt{Span}((1,0,2),(0,1,-3))$

### W={(x,y,2x-3y)}:x and y are real numbers.

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