vector space

Let $\mathbb{R}$ and $\mathbb{R}^3$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors...

If $\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}} \ldots \mathbf{v}_{\mathbf{6}}$ are six vectors in $\mathbb{R}^4$, which one of the statements is FALSE?

If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \right)$$ form an orthogonal basis of the three dimensional real...