Subspace in R^4: Investigating (2x+3y, x, 0, 1) as a Potential Subspace

[saintdick]

Homework Statement

Is this a subspace of R^4, (2x+3y, x, 0 , 1) . Give reasons

Homework Equations

The Attempt at a Solution

I am completely stuck at this one

 

[kru_]

A subset U of V is a subspace of V if it satisfies the properties needed to be a vector space: additive identity; closure under vector addition; closure under scalar multiplication.

Check that your given subset satisfies the properties.

a) Is there an additive identity from your set for R^4?

b) If you take two vectors from your given space, a and b, is a+b still in your set?

c) Is the scalar multiple of any vector in your set still in the set?

 

[HallsofIvy]

You might want to look particularly at the fourth component in a scalar product such as 2v.