where S = {[ 2a-b, a , b , -a ] | a,b are real numbers}
how do prove and show this one?
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 $\displaystyle \mathbb{R}^{4},$ it is two-dimensional at most.The vector $\displaystyle (2a-b,a,b,-a)$ is 4-dimensional and thus cannot belong to $\displaystyle \mathbb{R}^{3}.$