# Math Help - Is S = real space(R^3)

1. ## Is S = real space(R^3)

where S = {[ 2a-b, a , b , -a ] | a,b are real numbers}

how do prove and show this one?

2. Can you explain what you mean by real space( $\mathbb{R}^3$). I can't find that terminology in any of my algebra texts.

Are you asking if S forms a basis for $\mathbb{R}^3$?

3. Originally Posted by experiment00
where S = {[ 2a-b, a , b , -a ] | a,b are real numbers}

how do prove and show this one?

The vector $(2a-b,a,b,-a)$ is 4-dimensional and thus cannot belong to $\mathbb{R}^3$

Tonio

4. The vector $(2a-b,a,b,-a)$ is 4-dimensional and thus cannot belong to $\mathbb{R}^{3}.$
In addition, it is a vector with two degrees of freedom (it has two parameters, a and b). And so, considered as a subset of $\mathbb{R}^{4},$ it is two-dimensional at most.